chapter 1 1. (a) (b) (c) - knightstat.weebly.com

Statistics Final Exam Review 2014-2015

Chapter 1

1. The histograms below represent the distribution of five different data sets, each containing 28 integers, from

1 through 7, inclusive. The horizontal and vertical scales are the same for all graphs. Which graph

represents the data set with the largest standard deviation.

(A) (B) (C)

(D) (E)

2. The histogram below displays the times, in minutes, needed for each chimpanzee in a sample of 26 to

complete a simple navigational task.

It was determined that the largest observation, 93, is an outlier since Q3 + 1.5(Q3 Q1) = 87.125. Which of

the following boxplots could represent the information in the histogram?

(A) (B) (C)

(D) (E)


3. A botanist is studying the petal lengths, measured in millimeters, of two species of lilies. The boxplots

above illustrate the distribution of petal lengths from two samples of equal size, one from species A and the

other from species B. Based on these boxplots, which of the following is a correct conclusion about the data

collected in this study?

(A) The interquartile ranges are the same for both samples.

(B) The spread for species B is greater than the range for species A.

(C) There are more petal lengths that are greater than 70 mm for species A than there are for species B.

(D) There are more petal lengths that are greater than 40 mm for species B than there are for species A.

(E) There are more petal lengths that are less than 30 mm for species B than there are for species A.

4. The statistics below provide a summary of the distribution of heights, in inches, for a simple random sample

of 200 young children.

Mean: 46 inches Median: 45 inches Standard Deviation: 3 inches

First Quartile: 43 inches Third Quartile: 48 inches

About 100 children in the sample have heights that are

(A) less than 43 inches

(B) less than 48 inches

(C) between 43 and 48 inches

(D) between 40 and 52 inches

(E) more than 46 inches

5. A professor teaches two statistics classes. The morning class has 25 students and their average on the first

test was 82. The evening class has 15 students and their average on the same test was 74. What is the

average on this test if the professor combines the scores for both classes?

(A) 76 (B) 78 (C) 79 (D) 80 (E) cannot be calculated

6. An outlier is an observation that

(A) is seen more frequently than the other observations in the data set.

(B) is seen less frequently than the other observations in the data set.

(C) is always smaller than the other observations in the data set.

(D) is always larger than the other observations in the data set.

(E) is significantly different from the other observations in the data set.


7. The graph below displays the score of 32 students on a recent exam. 6 * *

6 * *

7 * * *

7 * * * *

8 * * * *

8 * * * * * *

9 * * * * * * *

9 * * * *

Which of the following statements is true?

(A) The mean will be higher than the median because the stemplot is skewed left.

(B) The median will be higher than the mean because the stemplot is skewed left.

(C) The mean will be higher than the median because the stemplot is skewed right.

(D) The median will be higher than the mean because the stemplot is skewed right.

(E) The mean and median will be approximately the same because the stemplot is symmetrical.

8. A random sample of 25 households from the Mountainview School District was surveyed. In this survey,

data were collected on the age of the youngest child living in each household. The histogram below

displays the data collected in the survey.

In which of the following intervals is the median of these data located?

(A) 0 years old to less than 2 years old

(B) 4 years old to less than 6 years old

(C) 6 years old to less than 8 years old

(D) 8 years old to less than 10 years old

(E) 10 years old to less than 12 years old

9. You measure the age, marital status and earned income of an SRS of 1463 women. The number and type of

variables you have measured is

(a) 1463; all quantitative.

(b) four; two categorical and two quantitative.

(c) four; one categorical and three quantitative.

(d) three; two categorical and one quantitative.

(e) three; one categorical and two quantitative.

Scores on this exam ranged from

64 to 95 points.


10. Consumers’ Union measured the gas mileage in miles per gallon of 38 1978–1979 model automobiles on a

special test track. The pie chart below provides information about the country of manufacture of the model

cars used by Consumers Union. Based on the pie chart, we may conclude that:

(a) Japanese cars get significantly lower gas mileage than cars of other countries. This is

because their slice of the pie is at the bottom of the chart.

(b) U.S cars get significantly higher gas mileage than cars from other countries.

(c) Swedish cars get gas mileages that are between those of Japanese and U.S. cars.

(d) Mercedes, Audi, Porsche, and BMW represent approximately a quarter of the cars tested.

(e) More than half of the cars in the study were from the United States.

11. A researcher reports that, on average, the participants in his study lost 10.4 pounds after two months on his

new diet. A friend of yours comments that she tried the diet for two months and lost no weight, so clearly

the report was a fraud. Which of the following statements is correct?

(a) Your friend must not have followed the diet correctly, since she did not lose weight.

(b) Since your friend did not lose weight, the report must not be correct.

(c) The report only gives the average. This does not imply that all participants in the study lost 10.4 pounds

or even that all lost weight. Your friend’s experience does not necessarily contradict the study results.

(d) In order for the study to be correct, we must now add your friend’s results to those of the study and

recompute the new average.

(e) Your friend is an outlier.

12. The following is an ogive on the number of ounces of alcohol (one ounce is about 30 mL) consumed per

week in a sample of 150 students.

A study wished to classify the students as “light”, “moderate”, “heavy” and “problem” drinkers by the

amount consumed per week. About what percentage of students are moderate drinkers, that is consume

between 4 and 8 ounces per week?

(a) 60%

(b) 20%

(c) 40%

(d) 80%

(e) 50%


13. Which of the following is likely to have a mean that is smaller than the median?

(a) The salaries of all National Football League players.

(b) The scores of students (out of 100 points) on a very easy exam in which most get nearly perfect scores

but a few do very poorly.

(c) The prices of homes in a large city.

(d) The scores of students (out of 100 points) on a very difficult exam in which most get poor scores but a

few do very well.

(e) Amounts awarded by civil court juries.

14. There are three children in a room, ages three, four, and five. If a four-year-old child enters the room the

(a) mean age will stay the same but the variance will increase.

(b) mean age will stay the same but the variance will decrease.

(c) mean age and variance will stay the same.

(d) mean age and variance will increase.

(e) mean age and variance will decrease.

15. The weights of the male and female students in a class are summarized in the following boxplots:

Which of the following is NOT correct?

(a) About 50% of the male students have weights between 150 and 185 pounds.

(b) About 25% of female students have weights more than 130 pounds.

(c) The median weight of male students is about 162 pounds.

(d) The mean weight of female students is about 120 pounds because of symmetry.

(e) The male students have less variability than the female students.


Chapter 2

1. In a certain southwestern city the air pollution index averages 62.5 during the year with a standard deviation

of 18.0. Assuming that the 68-95-99.7% rule is appropriate, the index falls within what interval about 95%

of the time?

(A) (8.5, 116.5) (B) (26.5, 98.5) (C) (26.5, 116.5) (D) (44.5, 80.5) (E) (44.5, 98.5)

2. A distribution of test scores is not symmetric. Which of the following is the best estimate of the z-score of

the third quartile?

(A) 0.67 (B) 0.75 (C) 1.00 (D) 1.41

(E) This z-score cannot be estimated from the information given.

3. Which of the following histograms would be best approximated by a normal distribution?

(a) (b) (c)

(d) (e)

4. Suppose that the distribution of math SAT scores from your state this year is normally distributed with mean

480 and standard deviation 100 for males, and mean 440 and standard deviation 120 for females. If someone

who scores 779 or higher on math SAT can be considered a genius, what is the percent of geniuses among

the male SAT takers?

(a) % (b) 14% (b) 3% (d) 1.4% (e) 0.14%

5. The average number of calories in ILUV candy bars is 210, with a standard deviation of 10. If the number

of calories per candy bar is normally distributed, what percent of candy bars contain more than 225 calories?

(A) 66.8% (B) 47.7% (C) 43.3% (D) 6.68% (E) 3.34%


6. A certain type of remote-control car has a fully charged battery at the time of purchase. The distribution of

running times of cars of this type, before they require recharging of the battery for the first time after its

period of initial use, is approximately normal with a mean of 80 minutes and a standard deviation of 2.5

minutes. The shaded area in the figure below represents which of the following probabilities?

(A) The probability that the running time of a randomly selected car of this type, before it requires

recharging of the battery for the first time, is between 75 minutes and 82.5 minutes.

(B) The probability that the running time of a randomly selected car of this type, before it requires

recharging of the battery for the first time, is between 75 minutes and 85 minutes.

(C) The probability that the running time of a randomly selected car of this type, before it requires

recharging of the battery for the first time, is between 77.5 minutes and 82.5 minutes.

(D) The probability that the running time of a randomly selected car of this type, before it requires

recharging of the battery for the first time, is between 77.5 minutes and 85 minutes.

(E) The probability that the running time of a randomly selected car of this type, before it requires

recharging of the battery for the first time, is between 77.5 minutes and 87.5 minutes.

7. Suppose that sixteen-ounce bags of chocolate chips cookies are produced with an actual mean weight of

16.1 ounces and a standard deviation of 0.1 ounce. The percentage of bags that will contain between 16.0

and 16.1 ounces is

(a) 2.35

(b) 0.15

(c) 34

(d) 50

(e) 13.5

8. The weights of a population of adult male gray whales are approximately normally distributed with a mean

weight of 18,000 kilograms and a standard deviation of 4,000 kilograms. The weights of a population of

adult male humpback whales are approximately normally distributed with a mean weight of 30,000

kilograms and a standard deviation of 6,000 kilograms. A certain adult male gray whale weighs 24,000

kilograms. This whale would have the same standardized weight (z-score) as an adult male humpback

whale whose weight, in kilograms, is equal to which of the following?

(A) 21,000 (B) 24,000 (C) 30,000 (D) 36,000 (E) 39,000


9. Population P1 and P2 are both normally distributed. The standard deviation of P1 is 5 with a mean of 23

while the standard deviation of P2 is 10 with a mean of 17. What can be said about the percentage of

observations falling within one standard deviation of the mean for each population?

(A) The percentage for P1 is twice the percentage for P2.

(B) The percentage for P1 is greater, but not twice as great, as the percentage for P2.

(C) The percentage for P2 is twice the percentage for P1.

(D) The percentage for P2 is greater, but not twice as great, as the percentage for P1.

(E) The percentages are identical.

10. Lauren is enrolled in a very large college calculus class. On the first exam, the class mean was 75 and the

standard deviation was 10. On the second exam, the class mean was 70 and the standard deviation was 15.

Lauren scored 85 on both exams. Assuming the scores on each exam were approximately normally

distributed, on which exam did Lauren score better relative to the rest of the class?

A) She scored much better on the first exam.

B) She scored much better on the second exam.

C) She scored about equally well on both exams.

D) It is impossible to tell because the class size is not given.

E) She should be taking Statistics, not Calculus.


Chapter 3

1. The equation of the least squares regression line for the points on the scatterplot above is xy 73.3.1ˆ .

What is the residual for the point (4, 7)?

(A) 2.78 (B) 3.00 (C) 4.00 (D) 4.22 (E) 7.00

2. A least squares regression line was fitted to the weights (in pounds) versus age (in months) of a group of

many young children. The equation of the line is ̂ , where. ̂ is the predicted weight and is the age of the child. Which of the following best describes the meaning of the slope of the least squares regression line? (A) For each increase in 1 month, the estimated weight increases by 16.6 pounds. (B) For each increase in 1 pound, the estimated age increases by 16.6 months. (C) For each increase in 1 month, the estimated weight increases by 0.65 pounds. (D) For each increase in 1 pound, the estimated age increases by 0.65 months. (E) The slope has no meaning because the units of measure for x and y are not the same.

3. Which of the following scatterplots could represent a data set with a correlation coefficient of 1r ?

0

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8 x

y

(A) (B) (C)

(D) (E)


4. In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was y = 10 + .9x where y is the final exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam?

(a) 95 (b) 85.5 (c) 90 (d) 95.5 (e) 99 5. Refer to the previous problem. On the final exam Carla scored 98. What is the value of her residual? (a) 98 (b) 2.5 (c) –2.5 (d) 0 (e) -1 6. All but one of the following statements contains a blunder. Which statement is correct? (a) There is a correlation of 0.54 between the position a football player plays and their weight. (b) The correlation between planting rate and yield of corn was found to be r=0.23. (c) The correlation between the gas mileage of a car and its weight is r=0.71 MPG. (d) We found a high correlation (r=1.09) between the height and age of children. (e) We found a correlation of r=–.63 between gender and political party preference. 7. In regression, the residuals are which of the following? (a) Those factors unexplained by the data (b) The difference between the observed responses and the values predicted by the regression line (c) Those data points which were recorded after the formal investigation was completed (d) Possible models unexplored by the investigator (e) An observation distinctly different from the rest of the observations. 8. What does the square of the correlation (r

2) measure?

(a) The slope of the least squares regression line (b) The intercept of the least squares regression line (c) The extent to which cause and effect is present in the data (d) The percent of the variation in the values of y that is explained by least-squares regression on the other. (e) The percent of the values of y that is explained by least-squares regression on the other. 9. Suppose we fit the least squares regression line to a set of data. What is true if a plot of the residuals shows a curved pattern? (a) The LSRL is not a good model for the data. (b) The correlation must be 0. (c) The correlation must be positive. (d) Outliers must be present. (e) R-Square must be 100%.


Raoul performed an experiment using 16 windup rubber band single-propeller airplanes. He wound up the propeller a different number of times and recorded the amount of time (in seconds) that the airplane flew for each number of rotations that the propeller was wound. A regression analysis was performed and the partial computer output is given below.

10. What is the equation of the least squares regression line?

(A) predicted time = 0.9241 + 0.04625 rotation (B) predicted rotation = 0.4625 + 0.9241 time (C) constant = 0.9241 + 0.6413x (D) predicted time = 0.6413 + 0.01565 rotation (E) predicted rotation = 0.01565 + 0.6413 time

11. What is the correlation coefficient? (A) 0.34 (B) 0.384 (C) 0.5426 (D) .6196 (E) 6.196 12. The sand lance is a small fish that can be found in the Northwest Atlantic. In a 10-year study, data were collected on the mean

length of specimens and their age (Canadian Journal of Fisheries and Aquatic Sciences, Vol. 40). The average age of the specimens was found to be 5 years with a standard deviation of 2.16 years and the average length was found to be 220.29 mm with a standard deviation of 27.99 mm. What is the slope of the regression line predicting the mean length if r = .98? (A) 0.1 mm (B) 12.7 mm (C) 13.0 mm (D) 27.4 mm (E) Not enough information

Lydia and Bob were searching the Internet to find information on air travel in the United States. They found

data on the number of commercial aircraft flying in the United States during the years 1990-1998. The dates

were recorded as years since 1990. Thus, the year 1990 was recorded as year 0. They fit a least squares

regression line to the data. The graph of the residuals and part of the computer output for their regression are

given below.

Predictor Coef Stdev t-ratio p

Constant 2939.93 20.55 143.09 0.000

Years 233.517 4.316 54.11 0.000


13. What is the proper interpretation for the y-intercept in context of this situation.

(A) In 1990, there were approximately 2,939.9 commercial aircraft flying in the United States.

(B) When time is zero, the number of commercial aircraft flying was 2939.93 in the United States.

(C) In 1990, there were approximately 233.517 commercial aircraft flying in the United States.

(D) When time is zero, the number of commercial aircraft flying was 233.517 in the United States.

(E) The y-intercept does not make sense in the context of this problem.

14. A study found correlation r = 0.61 between the sex of a worker and his or her income. You conclude that

(a) Women earn more than men on the average.

(b) Women earn less than men on average.

(c) An arithmetic mistake was made; this is not a possible value of r.

(d) This is nonsense because r does not make sense in this situation.

(e) Women earn 11% less than men on average.

15. If dataset A of (x,y) data has correlation coefficient r = 0.65, and a second dataset B has correlation

r = –0.65, then

(a) The points in A exhibit a stronger linear association than B.

(b) The points in B exhibit a stronger linear association than A.

(c) Neither A nor B has a stronger linear association.

(d) You can’t tell which dataset has a stronger linear association without seeing the data or seeing the scatterplots.

(e) The residual plots must each have a uniform pattern.


Chapter 4

1. Suppose we fit the least squares regression line to a set of data. What do we call any individual points with unusually large values

of the residuals?

(a) Response variables

(b) The slope

(c) Outliers

(d) Correlations

(e) None of the above

2. The effect of removing the right-most point (near the positive x-axis) in the scatterplot shown would be:

(a) The slope of the LSRL will increase; r will increase

(b) The slope of the LSRL will increase; r will decrease

(c) The slope of the LSRL will decrease; r will increase

(d) The slope of the LSRL will decrease; r will decrease

(e) No change

3. If removing an observation from a data set would have a marked change on the position of the LSRL fit to the data, what is the

point called:

(a) Robust

(b) A residual

(c) A response

(d) Influential


4. Suppose the correlation between two variables x and y is due to the fact that both are responding to changes in some unobserved

third variable. What is this due to?

(a) Cause and effect between x and y

(b) The effect of a lurking variable

(c) Extrapolation

(d) Common sense

(e) None of the above. The answer is .

5. Suppose a straight line is fit to data having response variable y and explanatory variable x. Predicting values of y for values of

x outside the range of the observed data is called

(a) Correlation

(b) Causation

(c) Extrapolation

(d) Sampling

(e) None of the above. The answer is .

6. There is a positive association between the number of drownings and ice cream sales. This is an example of

an association likely caused by:

(a) Coincidence

(b) Cause and effect relationship

(b) Confounding factor

(d) Common response



7. If the correlation between body weight and annual income were high and positive, we could conclude that:

(a) High incomes cause people to eat more food.

(b) Low incomes cause people to eat less food.

(c) High-income people tend to spend a greater proportion of their income on food than low-income people,

on average.

(d) High-income people tend to be heavier than low income people, on average.

(e) High incomes cause people to gain weight.

8. A study examined the relationship between the sepal length and sepal width for two varieties of an exotic

tropical plant. Varieties A and B are represented by x's and o's, respectively, in the following plot:

Which of the following statements is FALSE?

(a) Considering variety A alone, there is a negative correlation between sepal length and sepal width.

(b) Considering variety B alone, the least squares regression line for predicting sepal length from sepal

width has a negative slope.

(c) Considering both varieties together, there is a positive correlation between sepal length and sepal width.

(d) Considering each variety separately, there is a positive correlation between sepal length and sepal width.

(e) Considering both varieties together, the least squares regression line for predicting sepal length from

sepal width has a positive slope.

9. From tax records, it is relative easy to determine the amount of liquor consumed per capita and the number

of cigarettes consumed per capita for each of the 10 provinces of Canada. These are plotted on a scatterplot

and a high positive correlation is found. Which of the following is correct?

(a) This implies that heavy smoking causes people to drink more.

(b) This implies that heavy drinking causes people to smoke more.

(b) We cannot conclude cause and effect, but this also implies that there is a high positive correlation

between cigarette smoking and alcohol consumption for individuals.

(d) This could be an example of a correlation caused by a common cause because both activities are highly

correlated with average family income and average income varies widely among the provinces.

(e) We cannot conclude cause and effect, but this also implies that the same individuals both smoke and

consume liquor.


10. Asia has become a major competitor of the U.S. and Western Europe in education as well as economics. Here are counts of first

university degrees in science and engineering the three regions. Using the two-way table below, what percent of Western

European degrees are natural science / what percent of engineering degrees are Asian?

Field United States Western Europe Asia Totals

Engineering 61,941 158,931 280,772 501,644

Natural science 111,158 140,126 242,879 494,163

Social science 182,166 116,353 236,018 534,537

Totals 355,285 415,410 759,669 1,530,364

a) 34% / 37% b) 28% / 37% c) 28% / 56% d) 34% / 56%

11. Two measures x and y were taken on 18 subjects. The first of two regressions, Regression I, yielded . .y x 24 5 161 and had the following residual plot.

The second regression, Regression II, yielded ˆlog( ) 1.6 0.51 log( )y x and had the following residual plot.

Which of the following conclusions is best supported by the evidence above?

a) There is a linear relationship between x and y, and Regression I yields a better fit.

b) There is a linear relationship between x and y, and Regression II yields a better fit.

c) There is a negative correlation between x and y.

d) There is a nonlinear relationship between x and y, and Regression I yields a better fit.

e) There is a nonlinear relationship between x and y, and Regression II yields a better fit.


Chapter 5

1. A member of Congress wants to know what his constituents think of proposed legislation on health insurance. His staff reports

that 228 letters have been received on the subject, of which 193 oppose the legislation. What is the population in this situation?

(a) The constituents (b) The 228 letters received (c) The 193 opposing the legislation (d) Congress (e) Those without health insurance

2. A television news editor would like to know how local registered voters would respond to the question,

"Are you in favor of the school bond measure that will be voted on in an upcoming special election?" A

television survey is conducted during a break in the evening news by listing two telephone numbers side by

side on the screen, one for viewers to call if they approve of the bond measure, and the other to call if they

disapprove. This survey method could produce biased results for a number of reasons. Which one of the

following is the most obvious reason?

(A) It uses a stratified sample rather than a simple random sample.

(B) People who feel strongly about the issue are more likely to respond.

(C) Viewers should be told about the issues before the survey is conducted.

(D) Some registered voters who call might not vote in the election.

(E) The wording of the question is biased. 3. We say that the design of a study is biased if which of the following is true? (a) A racial or sexual preference is suspected (b) Random placebos have been used (c) Certain outcomes are systematically favored (d) The correlation is greater than 1 or less than –1 (e) It is a planned study where deliberate conditions are imposed 4. Control groups are used in experiments in order to . . . (a) Control the effects of lurking variables such as the placebo effect (b) Control the subjects of a study so as to insure all participate equally (c) Guarantee that someone other than the investigators, who have a vested interest in the outcome, control how the

experiment is conducted (d) Achieve a proper and uniform level of randomization (e) Make sure each group has an equal number of participants

5. A nutritionist wants to study the effect of storage time (6, 12, and 18 months) on the amount of vitamin C

present in freeze dried fruit when stored for these lengths of time. Vitamin C is measured in milligrams per

100 milligrams of fruit. Six fruit packs were randomly assigned to each of the three storage times. The

treatment, experimental unit, and response are respectively: (a) A specific storage time, amount of vitamin C, a fruit pack (b) A fruit pack, amount of vitamin C, a specific storage time

(c) Random assignment, a fruit pack, amount of vitamin C

(d) A specific storage time, a fruit pack, amount of vitamin C

(e) A specific storage time, the nutritionist, amount of vitamin C


6. Suppose that 30 percent of the subscribers to a cable television service watch the shopping channel at least

once a week. You are to design a simulation to estimate the probability that none of five randomly selected

subscribers watches the shopping channel at least once a week. Which of the following assignments of the

digits 0 through 9 would be appropriate for modeling an individual subscriber's behavior in this simulation?

(A) Assign "0, 1, 2" as watching the shopping channel and "3, 4, 5, 6, 7, 8, and 9" as not watching,

(B) Assign "0, 1, 2, 3" as watching the shopping channel and "4, 5, 6, 7, 8, and 9" as not watching.

(C) Assign "1, 2, 3, 4, 5" as watching the shopping channel a and "6, 7 , 8, 9, and 0" as not watching.

(D) Assign "0" as watching the shopping channel and "1, 2, 3, 4, and 5" as not watching; ignore digits "6, 7,

8, and 9,"

(E) Assign "3" as watching the shopping channel and "0, 1, 2, 4, 5, 6, 7, 8, and 9" as not watching.7.

7. We wish to draw a sample of size 5 without replacement from a population of 50 households. Suppose the

households are numbered "01", "02", …, "50", and suppose that the relevant line of the random number table

is: 11362 35692 96237 90842 46843 62719 64049 17823

Then the households selected are: (a) Households 11 13 36 62 73 (b) Households 11 36 23 08 42 (c) Households 11 36 23 23 08 (d) Households 11 36 23 56 92 (e) Households 11 35 96 90 46

8. An electronics firm wants to survey its employees to determine their attitudes toward employee

compensation. They obtain the sample for the survey by randomly selecting one of the first 20 names on an

alphabetical list of employees and then select each 20th

name on the list from then on. This is an example of

which of the following:

(a) Simple random sample

(b) Cluster random sample

(c) Convenience sample

(d) Stratified random sample

(e) Systematic random sample

9. Automobile brake pads are either metallic or nonmetallic. An experiment is to be conducted to determine

whether the stopping distance is the same for both types of brake pads. In previous studies, it was determined

that car size (small, medium, large) is associated with stopping distance, but car type (sedan, wagon, coupe) is

not associated with stopping distance. The experiment would be best done

(A) by blocking on car size

(B) by blocking on car type

(C) by blocking on stopping distance

(D) by blocking on brake pad type

(E) without blocking


10. Suppose that 30 percent of the subscribers to a cable television service watch the shopping channel at least

once a week. You are to design a simulation to estimate the probability that none of five randomly selected

subscribers watches the shopping channel at least once a week. Which of the following assignments of the

digits 0 through 9 would be appropriate for modeling an individual subscriber's behavior in this simulation?

(A) Assign "0, 1, 2" as watching the shopping channel and "3, 4, 5, 6, 7, 8, and 9" as not watching,

(B) Assign "0, 1, 2, 3" as watching the shopping channel and "4, 5, 6, 7, 8, and 9" as not watching.

(C) Assign "1, 2, 3, 4, 5" as watching the shopping channel a and "6, 7 , 8, 9, and 0" as not watching.

(D) Assign "0" as watching the shopping channel and "1, 2, 3, 4, and 5" as not watching; ignore digits "6, 7,

8, and 9,"

(E) Assign "3" as watching the shopping channel and "0, 1, 2, 4, 5, 6, 7, 8, and 9" as not watching.

11. A researcher wishes to test a new drug developed to treat hypertension (high blood pressure). A group of

40 hypertensive men and 60 hypertensive women is to be used. The experimenter randomly assigns 20 of

the men and 30 of the women to the placebo and assigns the rest to the treatment. The major reason for

separate assignment for men and women is that

(A) it is a large study with 100 subjects

(B) the new drug may affect men and women differently

(C) the new drug may affect hypertensive and nonhypertensive people differently

(D) this design uses matched pairs to detect the new-drug effect

(E) there must be an equal number of subjects in both the placebo group and the treatment group.

12. Which of the following is NOT a characteristic of stratified random sampling?

(A) Random sampling is part of the sampling procedure.

(B) The population is divided into groups of units that are similar on some characteristic.

(C) The strata are based on facts known before the sample is selected.

(D) Each individual unit in the population belongs to one and only one of the strata.

(E) Every possible subset of the population, of the desired sample size, has an equal chance of being

selected.


Chapter 6

1. The probability of any outcome of a random phenomenon is

(a) The precise degree of randomness present in the phenomenon

(b) Any number as long as it is between 0 and 1

(c) Either 0 or 1, depending on whether or not the phenomenon can actually occur or not

(d) The proportion of a very long series of repetitions on which the outcome occurs

2. Which of the following pairs of events are disjoint (mutually exclusive)?

(a) A: the odd numbers; B: the number 5

(b) A: the even numbers; B: the numbers greater than 10

(c) A: the numbers less than 5; B: all negative numbers

(d) A: the numbers above 100; B: the numbers less than –200

(e) A: negative numbers; B: odd numbers

3. If you choose a card at random from a well-shuffled deck of 52 cards, what is the probability that the

card chosen is not a heart?

(a) 0.25

(b) 0.50

(c) 0.75

(d) 1

4. Which of the following are true?

I. The sum of the probabilities in a probability distribution can be any number between 0 and 1.

II. The probability of the union of two events is the sum of the probabilities of those events.

III. The probability that an event happens is equal to 1 – (the probability that the event does not

happen).

(a) I and II only

(b) I and III only

(c) II and III only

(d) I, II, and III

5. If P(A) = 0.24 and P(B) = 0.52 and A and B are independent, what is P(A or B)?

(Hint: Draw a Venn diagram)

(a) 0.1248

(b) 0.28

(c) 0.6352

(d) 0.76


6. If a peanut M&M is chosen at random, the chances of it being of a particular color are shown in the table

below.

Color Brown Red Yellow Green Orange Blue

Probability .3 .2 .2 .2 .1

The probability of randomly drawing a blue peanut M&M is

(a) 0.1

(b) 0.2

(c) 0.3

(d) 1.0

(e) According to this distribution, it’s impossible to draw a blue peanut M&M.

7. Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B are disjoint

(mutually exclusive), then

(a) P(A and B) = 0.16.

(b) P(A or B) = 1.0.

(c) P(A and B) = 1.0.

(d) P(A or B) = 0.16.

(e) Both A and B are true.


Chapter 7

1. A Federally Qualified Health Center (FQHC) serves any patient who enters the clinic regardless of their ability to pay. Fees for their care are adjusted based on their income, etc. In addition to primary medical care, FQHCs receive special government regulated pricing for the drugs they prescribe. Unfortunately, many of these clinics struggle to staff enough pharmacists to provide all of the support needed. Below is the approximate distribution for the number of full-time pharmacists found at a randomly selected FQHC in the United States.

0 1 2 3 4 5

( ) 0.25 0.40 0.15 0.11 0.08 0.01

X

P X

Find the probability that a randomly selected FQHC has three or more pharmacists.

(A) 0.01 (B) .08 (C) 0.11 (D) 0.19 (E) 0.20 2. Suppose X and Y are random variables with X

=400, X=7.5, Y

=160, Y=2.5. Given that X and Y are

independent variables, what are the expected value and variance of the random variable X – Y. (A) , -5.0 (B) , 0.0 (C) , (D) , (E) , 50.0

3. Suppose X is a random variable with mean µ. Suppose we observe X many times and keep track of the average of the observed

values. The law of large numbers says that (a) The value of µ will get larger and larger as we observe X. (b) As we observe X more and more, this average and the value of µ will get larger and larger. (c) This average will get closer and closer to µ as we observe X more and more often. (d) As we observe X more and more, this average will get to be a larger and larger multiple of µ. (e) None of the above 4. In a population of students, the number of calculators owned is a random variable X with P(X = 0) = 0.2, P(X = 1) = 0.6, and P(X = 2) = 0.2. The mean of this probability distribution is (a) 0 (b) 2 (c) 1 (d) 0.5 (e) .3

5. Refer to the previous problem. The standard deviation of this probability distribution is (a) 1 (b) 0.79 (c) 0.71 (d) 0.63 (e) 0.33


6. A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening to soothing

music. Let X be the number of puzzles completed successfully by a subject. X had the following distribution: X 1 2 3 4 Probability 0.2 0.4 0.3 0.1 Using the above data, what is the probability that a randomly chosen subject completes at least 3 puzzles in the five-minute

period while listening to soothing music? (a) 0.3 (b) 0.4 (c) 0.6 (d) 0.9 (e) 1.0 7. Using the above data, P(X < 3) is (a) 0.3 (b) 0.4 (c) 0.6 (d) 0.9 (e) 0.0 8. Using the above data, the mean µ of X is (a) 2.0 (b) 2.3 (c) 2.5 (d) 3.0 (e) The answer cannot be computed from the information given. 9. Suppose X is a continuous random variable taking values between 0 and 2 and having the probability density function below. P(1 ≤ X ≤ 2) has value (a) 0.50. (b) 0.33 (c) 0.25 (d) 0.00 (e) 0.75

10. Which of the following random variables should be considered continuous? (a) The time it takes for a randomly chosen woman to run 100 meters (b) The number of brothers a randomly chosen person has (c) The number of cars owned by a randomly chosen adult male (d) The number of orders received by a mail order company in a randomly chosen week (e) The number of t-shirts you have bought this year


Chapter 8

1. In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random

sample of 30 students from this population, the probability that exactly 4 students have experienced math anxiety is (a) 0.8674 (b) 0.1325 (c) 0.2552 (d) 0.1024 (e) 0.8974 2. Refer to the previous problem. The standard deviation of the number of students in the sample who have experienced math

anxiety is (a) 4.8 (b) 2.19 (c) 6.0 (d) 150 (e) 0.0067 3. In a certain large population, 30% of households have a total annual income of $75,000. A simple random sample of 5 of these

households is selected. What is the probability that 2 or more of the households in the survey have an annual income of over $75,000?

(a) 0.3456 (b) 0.4718 (c) 0.6399 (d) 0.3602 (e) 0.1631 4. A factory makes silicon chips for use in computers. It is known that about 80% of the chips meet specifications. Every hour a

sample of 16 chips is selected at random for testing. Assume a binomial distribution is valid. Suppose we collect a large number of these samples of 16 chips and determine the number meeting specifications in each sample. What is the approximate mean of the number of chips meeting specifications?

(a) 16.20 (b) 12.8 (c) 3.2 (d) 20

(e) 10.8 5. The expected value (mean) of a geometric random variable is determined by the formula (1 – p)

n .

(a) True (b) False 6. An important difference between binomial and geometric random variables is that there is a fixed number of trials in a binomial

setting, and the number of trials varies in a geometric setting. (a) True (b) False


7. In a certain large population, 55% of households have a total annual income of over $50,000. A simple random sample is taken of 20 of these households. Let X be the number of households in the sample with an annual income of over $50,000 and assume that the binomial assumptions are reasonable. What is the mean of X?

(a) 5.5 (b) 9 (c) 11 (d) 27,500 (e) 36 8. 25% of all trucks undergoing a certain inspection will fail the inspection. Assume that trucks are independently undergoing this

inspection, one at a time. The expected number of trucks inspected before a truck fails inspection is (a) 2 (b) 4 (c) 5 (d) 20

(e) 25

9. The probability that a certain machine will produce a defective item is 0.15. If a random sample of 6 items is taken from the

output of this machine, what is the standard deviation? (a) 0.8746 (b) 0.7650 (c) 6.6667 (d) 0.9000 (e) 0.9487 10. The expected value (mean) of a binomial random variable is determined by the formula .

(a) True (b) False


Chapter 9

1. An internet survey conducted by cnn.com reported that 68% of those who responded to the survey planned to vote in the next gubernatorial election. The unknown true percentage of American citizens who plan to vote in the next gubernatorial election is a

(a) Statistic

(b) Sample

(c) Parameter

(d) Population

2. The distribution of all possible values for a given sample size for a fixed population is a

(a) population proportion

(b) sampling distribution

(c) random survey

(d) sample proportion

3. The number of graduate students at Harvard University is approximately 14,500, while the number at

Howard University is approximately 3300. At both schools a simple random sample of about 2% of the

graduates is taken. Which of the following is the best conclusion?

(a) The sample from Harvard has less sampling variability than that from Howard.

(b) The sample from Harvard has more sampling variability than that from Howard.

(c) The sample from Harvard has almost the same sampling variability as that from Howard.

(d) It is impossible to make any statement about the sampling variability of the two samples since the

students surveyed were different.

4. About 17% of all US households own a Blu Ray player. A simple random sample of 100 households is to

be contacted and the sample proportion computed. What is the standard deviation of the sampling

distribution of the sample proportion?

(a) 0.03756

(b) 0.001411

(c) 3.756

(d) 0.01411

5. The mean number of days a house in a large population is on the market before it sells is 63 with a standard

deviation of 14. Suppose 100 houses are randomly selected for real estate research. The distribution of the

sample mean is

(a) Exactly normal, mean 63, standard deviation 14.

(b) Approximately normal, mean 63, standard deviation 1.4.

(c) Approximately normal, mean 63, standard deviation 0.14.

(d) Approximately normal, mean 63, standard deviation 14.

(e) Exactly normal, mean 63, standard deviation 1.4.


6. As the sample size increases, the shape of the sampling distribution will

A) stay the same

B) taller and more narrow

C) become strongly skewed right

D) shorter and wider

7. As the sample size increases, the spread of the sampling distribution will?

A) decrease

B) increase

C) stay the same

Use the following situation to answer the next two multiple choice questions.

In the fall of 2010, 72% of the almost 7,500 first-year freshman attending the University of Texas had strong

enough math skills to take an entry level course.

8. Based on a sample of 20 students, can we assume our calculations will be accurate?

A) Yes, all requirements are met to use the normal approximation.

B) Maybe, it depends on the value of p we are using.

C) No, one of the conditions is not met.

D) No, two of the conditions are not met.

9. What value will we use for the standard deviation for a sample of 100 students?

(Hint: Use the ̂ formula for standard deviation.)

A) .00201 B) .0045 C) .0449 D) .0201 E) not enough information

chapter 1 1. (a) (b) (c) - knightstat.weebly.com

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