Family Feud Review

Math 2200: Elementary Statistics

April 13, 2011

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Question 1

Suppose you obtain a test statistic with an associated p-value of0.025. Assuming a 5% significance level for the hypothesis test,you should decide to

A. Fail to reject H1

B. Reject H1

C. Fail to reject H0

D. Reject H0

E. There is not sufficient information to determine a decision

Moore Family Feud

Question 1

Suppose you obtain a test statistic with an associated p-value of0.025. Assuming a 5% significance level for the hypothesis test,you should decide to

A. Fail to reject H1

B. Reject H1

C. Fail to reject H0

D. Reject H0

E. There is not sufficient information to determine a decision

Moore Family Feud

Question 1

Suppose you obtain a test statistic with an associated p-value of0.025. Assuming a 5% significance level for the hypothesis test,you should decide to

A. Fail to reject H1

B. Reject H1

C. Fail to reject H0

D. Reject H0

E. There is not sufficient information to determine a decision

Moore Family Feud

Question 1

Suppose you obtain a test statistic with an associated p-value of0.025. Assuming a 5% significance level for the hypothesis test,you should decide to

A. Fail to reject H1

B. Reject H1

C. Fail to reject H0

D. Reject H0

E. There is not sufficient information to determine a decision

Moore Family Feud

Question 1

Suppose you obtain a test statistic with an associated p-value of0.025. Assuming a 5% significance level for the hypothesis test,you should decide to

A. Fail to reject H1

B. Reject H1

C. Fail to reject H0

D. Reject H0

E. There is not sufficient information to determine a decision

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Answer 1

AnswerD. Reject H0

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Question 2

Suppose the null and alternative hypothesis are given by thefollowing statements

H0 : µ = 73

H1 : µ 6= 73.

What is the p-value if the test statistic is given by z = −1.8753?

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Answer 2

Answer.0607513341

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Question 3

Assume the margin of error for a confidence interval is 12. What isthe length of the interval?

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Answer 3

Answer24

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Question 4

Suppose you want a 95% confidence level for a range of averagesalaries for those individuals that have taken a statistics courseduring their college career. You know the standard deviation ofthese individuals is $8463. Assuming you found 100 individualswith a statistics background have an average salary of $52000, findthe corresponding confidence interval. Write your answer ininterval notation.

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Answer 4

Answer(50341.28, 53658.72)

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Question 5

A courier service advertises that its average delivery time is 4 hoursfor local deliveries. A consumer advocate thinks it takes muchmore time. A random sample of times for 10 deliveries to anaddress across town was recorded. The data is shown below.

4.25 4.75 3.28 5.1 4.93.6 3.8 5.3 4.15 4.87

Compute the degrees of freedom involved with this distribution.

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Answer 5

Answer9

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Question 6

A courier service advertises that its average delivery time is 4 hoursfor local deliveries. A consumer advocate thinks it takes muchmore time. A random sample of times for 10 deliveries to anaddress across town was recorded. The data is shown below.

4.25 4.75 3.28 5.1 4.93.6 3.8 5.3 4.15 4.87

Test to determine whether there is enough evidence to support theconsumer group’s beliefs at the 1% significance level.

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Answer 6

Helpful Information

H0 : µ = 4

H1 : µ > 4

x = 4.4 s = .6857923236degrees of freedom = 9 α = .01

t = 1.84445206 p − value = .0491069665

AnswerFail to reject H0

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Answer 6

Helpful Information

H0 : µ = 4

H1 : µ > 4

x = 4.4 s = .6857923236degrees of freedom = 9 α = .01

t = 1.84445206 p − value = .0491069665

AnswerFail to reject H0

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Answer 6

Helpful Information

H0 : µ = 4

H1 : µ > 4

x = 4.4

s = .6857923236degrees of freedom = 9 α = .01

t = 1.84445206 p − value = .0491069665

AnswerFail to reject H0

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Answer 6

Helpful Information

H0 : µ = 4

H1 : µ > 4

x = 4.4 s = .6857923236

degrees of freedom = 9 α = .01t = 1.84445206 p − value = .0491069665

AnswerFail to reject H0

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Answer 6

Helpful Information

H0 : µ = 4

H1 : µ > 4

x = 4.4 s = .6857923236degrees of freedom = 9

α = .01t = 1.84445206 p − value = .0491069665

AnswerFail to reject H0

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Answer 6

Helpful Information

H0 : µ = 4

H1 : µ > 4

x = 4.4 s = .6857923236degrees of freedom = 9 α = .01

t = 1.84445206 p − value = .0491069665

AnswerFail to reject H0

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Answer 6

Helpful Information

H0 : µ = 4

H1 : µ > 4

x = 4.4 s = .6857923236degrees of freedom = 9 α = .01

t = 1.84445206

p − value = .0491069665

AnswerFail to reject H0

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Answer 6

Helpful Information

H0 : µ = 4

H1 : µ > 4

x = 4.4 s = .6857923236degrees of freedom = 9 α = .01

t = 1.84445206 p − value = .0491069665

AnswerFail to reject H0

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Answer 6

Helpful Information

H0 : µ = 4

H1 : µ > 4

x = 4.4 s = .6857923236degrees of freedom = 9 α = .01

t = 1.84445206 p − value = .0491069665

AnswerFail to reject H0

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Question 7

A company believes they have created a product that will receivenotoriety regardless of the education of an individual. Thiscompany hires a marketing research firm which suspects that thisparticular product has higher name recognition among collegegraduates than among high school graduates. A sample from eachpopulation is selected, and each asked if they have heard of theproduct in question. A summary of the sample sizes and number ofeach group answering “yes” are given below

High school graduates : n1 = 82, x1 = 58, s1 = 6

College graduates : n2 = 93, x2 = 62, s2 = 11

According to the information given above, what is the null andalternative hypothesis?

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Answer 7

Answer

H0 : µ1 = µ2

H1 : µ1 < µ2

where µ1 is the population mean for high school graduates and µ2

is the population mean for college graduates.

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Question 8

A company believes they have created a product that will receivenotoriety regardless of the education of an individual. Thiscompany hires a marketing research firm which suspects that thisparticular product has higher name recognition among collegegraduates than among high school graduates. A sample from eachpopulation is selected, and each asked if they have heard of theproduct in question. A summary of the sample sizes and number ofeach group answering “yes” are given below

High school graduates : n1 = 82, x1 = 58, s1 = 6

College graduates : n2 = 93, x2 = 62, s2 = 11

Find the p-value for the standardized test statistic that can beobtained from the above information.

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Answer 8

Helpful Information

t = −3.032305337

degrees of freedom = 145.7179701

Answerp − value = .0014367944

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Question 9

During the last 15 episodes of Jeopardy the winner of each showhad the dollar amounts listed below.

32100 12000 19200 20250 500541300 28275 23000 16775 300113700 48500 17700 18900 19750

If you were asked to estimate with 95% confidence the meanwinnings for all of Jeopardy’s players, what is the critical value forsuch a confidence interval?

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Answer 9

Answert∗ = 2.145

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Question 10

During the last 15 episodes of Jeopardy the winner of each showhad the dollar amounts listed below.

32100 12000 19200 20250 500541300 28275 23000 16775 300113700 48500 17700 18900 19750

Estimate with 95% confidence the mean winnings for all the showsplayers.

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Answer 10

Helpful Information

t∗ = 2.145

x = 21297.06667

s = 12246.75335

n = 15

Answer(14514.37, 28079.77)

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Question 11

We suspect that men are more prone to road rage than women. Tosee if this is true, test these hypotheses for the mean road ragescores of all male and female drives:

A. H0 : µm = µf and Ha : µm < µf

B. H0 : µm > µf and Ha : µm ≤ µf

C. H0 : µm = µf and Ha : µm > µf

D. H0 : µm = µf and Ha : µm 6= µf

E. None of the above

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Question 11

We suspect that men are more prone to road rage than women. Tosee if this is true, test these hypotheses for the mean road ragescores of all male and female drives:

A. H0 : µm = µf and Ha : µm < µf

B. H0 : µm > µf and Ha : µm ≤ µf

C. H0 : µm = µf and Ha : µm > µf

D. H0 : µm = µf and Ha : µm 6= µf

E. None of the above

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Question 11

We suspect that men are more prone to road rage than women. Tosee if this is true, test these hypotheses for the mean road ragescores of all male and female drives:

A. H0 : µm = µf and Ha : µm < µf

B. H0 : µm > µf and Ha : µm ≤ µf

C. H0 : µm = µf and Ha : µm > µf

D. H0 : µm = µf and Ha : µm 6= µf

E. None of the above

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Question 11

We suspect that men are more prone to road rage than women. Tosee if this is true, test these hypotheses for the mean road ragescores of all male and female drives:

A. H0 : µm = µf and Ha : µm < µf

B. H0 : µm > µf and Ha : µm ≤ µf

C. H0 : µm = µf and Ha : µm > µf

D. H0 : µm = µf and Ha : µm 6= µf

E. None of the above

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Question 11

We suspect that men are more prone to road rage than women. Tosee if this is true, test these hypotheses for the mean road ragescores of all male and female drives:

A. H0 : µm = µf and Ha : µm < µf

B. H0 : µm > µf and Ha : µm ≤ µf

C. H0 : µm = µf and Ha : µm > µf

D. H0 : µm = µf and Ha : µm 6= µf

E. None of the above

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Answer 11

AnswerC. H0 : µm = µf and Ha : µm > µf

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Question 12

We suspect that men are more prone to road rage than women. Tosee if this is true we ran the hypothesis tests listed in the previousslide. Determine the type of distribution that corresponds to thealternative hypothesis, state the number of tails, and determinethe location of the tails.

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Answer 12

Answert-distribution, one tail to the right

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Question 13

Determine whether the following symbols are parameters orstatistics:

σ, x , s, µ

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Answer 13

AnswerParameters: σ, µ

Statistics: x , s

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Question 14

A laboratory scale is known to have a standard deviation ofσ = 0.001 gram in repeated weighings. Scale readings in repeatedweighings are Normally distributed, with mean equal to the trueweight of the specimen. How many times must you weigh aspecimen on this scale in order to be within 0.0005 grams of theactual weight with 95% confidence.

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Answer 14

Helpful Information

σ = 0.001

z∗ = 1.960

Margin of error = 0.0005

Answern = 16

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Question 15

You are testing H0 : µ = 0 against H1 : µ 6= 0 based on a simplerandom sample of 15 observations from a Normal population.What region would correspond to a t-statistic of t = −3.326 whentrying to determine a p-value?

A. (−∞,−3.326)

B. (3.326,∞)C. (−3.326, 3.326)D. (−∞,−3.326) ∪ (∞, 3.326)E. (∞,−3.326) ∪ (3.326,∞)F. (−∞,∞)G. None of the above

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Question 15

You are testing H0 : µ = 0 against H1 : µ 6= 0 based on a simplerandom sample of 15 observations from a Normal population.What region would correspond to a t-statistic of t = −3.326 whentrying to determine a p-value?

A. (−∞,−3.326)B. (3.326,∞)

C. (−3.326, 3.326)D. (−∞,−3.326) ∪ (∞, 3.326)E. (∞,−3.326) ∪ (3.326,∞)F. (−∞,∞)G. None of the above

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Question 15

You are testing H0 : µ = 0 against H1 : µ 6= 0 based on a simplerandom sample of 15 observations from a Normal population.What region would correspond to a t-statistic of t = −3.326 whentrying to determine a p-value?

A. (−∞,−3.326)B. (3.326,∞)C. (−3.326, 3.326)

D. (−∞,−3.326) ∪ (∞, 3.326)E. (∞,−3.326) ∪ (3.326,∞)F. (−∞,∞)G. None of the above

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Question 15

You are testing H0 : µ = 0 against H1 : µ 6= 0 based on a simplerandom sample of 15 observations from a Normal population.What region would correspond to a t-statistic of t = −3.326 whentrying to determine a p-value?

A. (−∞,−3.326)B. (3.326,∞)C. (−3.326, 3.326)D. (−∞,−3.326) ∪ (∞, 3.326)

E. (∞,−3.326) ∪ (3.326,∞)F. (−∞,∞)G. None of the above

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Question 15

You are testing H0 : µ = 0 against H1 : µ 6= 0 based on a simplerandom sample of 15 observations from a Normal population.What region would correspond to a t-statistic of t = −3.326 whentrying to determine a p-value?

A. (−∞,−3.326)B. (3.326,∞)C. (−3.326, 3.326)D. (−∞,−3.326) ∪ (∞, 3.326)E. (∞,−3.326) ∪ (3.326,∞)

F. (−∞,∞)G. None of the above

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Question 15

You are testing H0 : µ = 0 against H1 : µ 6= 0 based on a simplerandom sample of 15 observations from a Normal population.What region would correspond to a t-statistic of t = −3.326 whentrying to determine a p-value?

A. (−∞,−3.326)B. (3.326,∞)C. (−3.326, 3.326)D. (−∞,−3.326) ∪ (∞, 3.326)E. (∞,−3.326) ∪ (3.326,∞)F. (−∞,∞)

G. None of the above

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Question 15

You are testing H0 : µ = 0 against H1 : µ 6= 0 based on a simplerandom sample of 15 observations from a Normal population.What region would correspond to a t-statistic of t = −3.326 whentrying to determine a p-value?

A. (−∞,−3.326)B. (3.326,∞)C. (−3.326, 3.326)D. (−∞,−3.326) ∪ (∞, 3.326)E. (∞,−3.326) ∪ (3.326,∞)F. (−∞,∞)G. None of the above

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Answer 15

AnswerG. None of the above

The correct region is (−∞,−3.326) ∪ (3.326,∞)

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Answer 15

AnswerG. None of the above

The correct region is (−∞,−3.326) ∪ (3.326,∞)

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Question 16

How well materials conduct heat matters when designing houses.Conductivity is measured in terms of watts of heat powertransmitted per square meter of surface per degree Celsius oftemperature difference on the two sides of the material. TheNational Institute of Standards and Technology (NIST) states thatglass has conductivity about 1. You have taken 11 measurementsof the heat conductivity of a particular type of glass and found themean to be 1.13 and a standard deviation of 0.22. Is theresignificant evidence at the 5% level that the mean conductivity ofthis type of glass differs from the consensus conductivity for glass?

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Answer 16

Helpful Information

µ = 1

x = 1.13

s = 0.22

n = 11

t = 1.95982374

p − value = 2P(T > 1.95982374) = .0784591899

AnswerNo, there is not sufficient evidence to reject H0 at the 5% significance level

Answer 2Fail to reject H0

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Question 17

Cola makers test new recipes for loss of sweetness during storage.Trained tasters rate the sweetness before and after storage. Thesweetness losses found by 10 tasters for one new cola recipe isgiven below.2.0 0.4 0.7 2.0 − 0.42.2 2.3 1.2 1.1 − 1.3If you want to determine if the data is good evidence that the colalost sweetness, then what are your null and alternative hypotheses?

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Answer 17

Answer

H0 : µ = 0

H1 : µ > 0

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Question 18

Cola makers test new recipes for loss of sweetness during storage.Trained tasters rate the sweetness before and after storage. Thesweetness losses found by 10 tasters for one new cola recipe isgiven below.2.0 0.4 0.7 2.0 − 0.42.2 2.3 1.2 1.1 − 1.3Determine if the data is good evidence that the cola lost sweetnessat the 2.5% significance level.

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Answer 18

Helpful Information

x = 1.02

s = 1.19604789

n = 10

t = 2.69668949

p − value = 0.0122631561

AnswerThere is significant evidence to reject H0 at the 2.5% significance level.

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