Entering Probability and Statistics

Summer Assignment TKCS-2016

Name:____________________________

Instructions:

• Show all work in a neat and organized manner. • You may receive help from any resource you want as long as you understand how to do each

problem o Recommended websites:

§ Math.com § www.miss-stow-math.wikispaces.com (you can utilized any subject flipped

classroom or not for help) § www.stattreck.com/tutorials/statistics-tutorial.aspx

• This packet must be completed and turned in the first day of school

Vocabulary:

Please use the Internet and/or any other resources to define each of the terms below. Try your best to search for definitions that would be applicable to statistics.

For example: the definition of populations could say: “the total number of persons inhabiting a country, city, or any district.” However, in a statistical setting, the correct definition would be “all subjects (human or otherwise) that are being studied.”

1. statistics

2. variable

3. data

4. random variables

5. descriptive statistics

6. population

7. sample

8. inferential statistics

9. probability

10. hypothesis testing

11. qualitative variables

12. quantitative variables

13. discrete variables

14. continuous variables

15. boundaries

16. median

17. mean

18. outlier

19. range

20. percentiles

21. random sampling

22. systematic sampling

23. stratified sampling

24. cluster sampling

25. convenience sampling

26. independent variable

27. dependent variable

28. control group

29. observational study

30. experimental study

31. In each of these statements, tell whether descriptive or inferential statistics have been used. a. In the year 2020, 148 million Americans will be enrolled in a health savings plan.

b. Drinking coffee daily can help reduce heart problems in the future.

c. Experts say mortgage rates may soon hit bottom.

d. The average sale price of homes in Monroe last year was $398,000.

32. Classify each variable as qualitative or quantitative a. Colors of cars in the faculty parking lot

b. Number of desks in the classroom

c. Number of pages in statistics textbooks

33. Classify each variable as discrete or continuous. a. Number of loaves of bread baked each day at a local bakery

b. Number of pizzas sold last year in the US

c. Weights of newborn infants at a certain hospital

34. Classify each sample as random, systematic, stratified, or cluster. a. In a large school district, all teachers from two buildings are interviewed to determine whether

they believe the students have less homework to do now than in previous years.

b. Every seventh customer entering a store is asked to answer a question.

c. Nursing supervisors are selected using random numbers in order to determine annual salaries.

d. Every 100th hamburger made is checked to determine fat content.

35. Information from research is sometimes taken out of context. Explain why the claims of these studies might be suspect. a. Only 15% of students surveyed watch the nightly news.

b. These new potato chips have half the fat.

c. Taking calcium will lower blood pressure in some people.

d. Three of four dentists recommend Brand X toothpaste.

36. For each study, identify whether it is observation or experimental, identify both the independent and dependent variables. a. A researcher stood at an intersection to see if the color of a car relates to running red lights.

b. Subjects are randomly assigned to four groups. Each group is placed on one of four special diets- a low-fat diet, a combination of the two, and a regular diet. After six months, the blood pressures of the groups are compared to see if diet has any effect on blood pressure.

Hint: When finding the probability of more than one event, there is a difference between using the word “and” vs “or”. If you need some help with this, then you can easily find the answer in Stattrek

37. A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 100 seniors, 150 juniors, and 200 sophomores who applied. Each senior’s name is placed in the lottery 3 times; each junior’s name, 2 times; and each sophomore’s name, 1 time. What is the probability that a senior’s name will be chosen?

a. !! b. !

! c . !

! d. !

! e . !

!

38. If a coin is tossed twice, what is the probability that on the first toss the coin lands heads and on the second toss the coin lands tails?

a. !! b. !

! c . !

! d. !

! e . 1

39. If a coin is tossed once, what is the probability that it will land either heads or tails?

40. Calculate the following probabilities and arrange them in order from least to greatest. a. The probability that a fair die will produce an even number.

b. A random digit from 1 to 9 (inclusive) is chosen, with all digits being equally likely. The probability that when it is squared it will end with the digit 1.

c. The probability that a letter chosen from the alphabet will be a vowel.

d. A random number between 1 and 20 (inclusive) is chosen. The probability that it’s square root will not be an integer.

Order:_______________, _______________, _______________, _______________

Here is a skill that is used often in Probability and Statistics

𝑨 =𝑩− 𝑪𝑫

41. If 𝐴 = 2.4,𝐵 = 102,𝑎𝑛𝑑 𝐶 = 100, what is D? Show your work.

42. If 𝐴 = −3.35,𝐵 = 60 𝑎𝑛𝑑 𝐷 = 4, what is C? Show your work.

If it expected that you have a thorough understanding of linear functions.

43. The USDA reported that in 1990 each person in the United States consumed an average of 133 pounds of natural sweeteners. They also claim this amount has decreased by about 0.6 pounds each year. a. Write a linear equation that relates years since 1990 to the average consumption of natural

sweeteners. Define your variables

b. What is the slope and what is the y-intercept?

c. Predict the average consumption of sweeteners per person for the year 2005.

44. The following equation can be used to predict the average height of boys anywhere between birth and 15 years old: 𝑦 = 2.79𝑥 + 25.64, where x is the age (in years) and y is the height (in inches). a. What does the slope represent in this problem? Interpret it in context.

b. What does the y-intercept represent in this problem? Interpret it in context.

45. Shopping Spree!

A marketing consultant observed 50 consecutive shoppers at a supermarket. One variable of interest was how much each shopper spent in the store. Here are the data (round to the nearest dollar), arranged in increasing order.

3 9 9 11 13 14 15 16 17 17

18 18 19 20 20 20 21 22 23 24

25 25 26 26 28 28 28 28 32 35

36 39 39 41 43 44 45 45 47 49

50 53 55 59 61 70 83 86 86 93

Make a stemplot using tens of dollars as the stem and dollars as the leaves. Be sure to include labels, a title, and a key.

46. Accidental Deaths

In 1997 there were 92,353 deaths from accidents in the United States. Among these were 42,340 deaths from motor vehicle accidents, 11,858 from falls, 10,163 from poisoning, 4,051 from drowning, and 3,601 from fires. The rest were listed as “other” causes.

a. Find the percent of accidental deaths from each of these causes, rounded to the nearest percent. b. What percent of accidental deaths were from “other” causes? c. Neatly create a well labeled bar graph of the distribution of causes of accidental deaths. Be sure to

include an “other causes” bar.

47. Statistics- What is that?

A statistic is a number calculated from data. Quantitative data has many different statistics that can be calculated. Determine the given statistics from the data below on the number of homeruns Mark McGuire has it in each season from 1982 to 2001.

70 52 22 49 3 32 58 39

39 65 42 29 9 32 9 33

Mean _____________________________

Minimum _______________________________

Quartile 1 (lower quartile) ______________________________

Median ____________________________

Quartile 3 (upper quartile) _____________________________

Maximum ______________________________

Range _________________________________

Interquartile Range ______________________________