Deck 17: Testing Hypotheses About Proportions

Question 1

According to the 2004 Canadian Community Health Survey,23.1% of Canadians aged 18 or older were considered obese; that is,they had a body mass index (BMI)of 30 or higher.Suppose you believe that the percentage of obese Canadians has increased since 2004 and wish to test your belief.A current survey in 2014 of 1000 random Canadians found that 245 were obese.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

A) $\mathrm { H } _ { 0 }$ : p = 0.231; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.231; z = -1.05; P-value = 0.1469.This data shows strong evidence of an increase from the 23.1% of obese Canadians.
B) $\mathrm { H } _ { 0 }$ : p = 0.231; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.231; z = -1.05; P-value = 0.8531.This data shows strong evidence of an increase from the 23.1% of obese Canadians.
C) $\mathrm { H } _ { 0 }$ : p = 0.231; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.231; z = 1.05; P-value = 0.1469.This data shows virtually no evidence of an increase from the 23.1% of obese Canadians.
D) $\mathrm { H } _ { 0 }$ : p = 0.231; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.231; z = -1.05; P-value = 0.0594.This data shows virtually no evidence of an increase from the 23.1% of obese Canadians.
E) $\mathrm { H } _ { 0 }$ : p = 0.231; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.231; z = 1.05; P-value = 0.8531.This data shows virtually no evidence of an increase from the 23.1% of obese Canadians.

Answer 1

$\mathrm { H } _ { 0 }$ : p = 0.231; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.231; z = 1.05; P-value = 0.1469.This data shows virtually no evidence of an increase from the 23.1% of obese Canadians.

Question 2

According to the 2004 Canadian Community Health Survey,23.1% of Canadians aged 18 or older were considered obese; that is,they had a body mass index (BMI)of 30 or higher.Suppose you believe that the percentage of obese Canadians has increased since 2004 and wish to test your belief.What are the null and alternative hypotheses?

A)H0: p = 0.231 HA: p < 0.231
B)H0: p = 0.231 HA: p ≠ 0.231
C)H0: p ≠ 0.231 HA: p = 0.231
D)H0: p = 0.231 HA: p > 0.231
E)H0: p < 0.231 HA: p > 0.231

Answer 2

H0: p = 0.231 HA: p > 0.231

Question 3

A hypothesis tests results in a large P-Value.Which conclusion is the best?

A)Accept the Null Hypothesis.
B)Fail to Reject the Alternative Hypothesis.
C)Reject the Null Hypothesis.
D)Fail to Reject the Null Hypothesis.
E)Accept the Alternative Hypothesis.

Answer 3

Fail to Reject the Null Hypothesis.

Question 4

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose that Statistics Canada claims that the current unemployment rate is lower than that of April 2011.Suppose a test was conducted on current unemployment and a random sample size of 1000 and found unemployment at 6.1%.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

A) $\mathrm { H } _ { 0 }$ : p = 0.076; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.076; z = -1.79; P-value = 0.9633.This data shows no evidence that the unemployment rate has decreased since April of 2011.
B) $\mathrm { H } _ { 0 }$ : p = 0.076; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.076; z = 1.79; P-value = 0.0367.This data shows very weak evidence that the unemployment rate has decreased since April of 2011.
C) $\mathrm { H } _ { 0 }$ : p = 0.076; $\mathrm { H } _ { \mathrm { A } }$ : p ? 0.076; z = -1.79; P-value = 0.0734.This data shows moderate evidence that the unemployment rate has decreased since April of 2011.
D) $\mathrm { H } _ { 0 }$ : p = 0.076; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.076; z = -1.79; P-value = 0.0367.This data shows strong evidence that the unemployment rate has decreased since April of 2011.
E) $\mathrm { H } _ { 0 }$ : p = 0.076; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.076; z = 1.79; P-value = 0.9633.This data shows strong evidence that the unemployment rate has decreased since April of 2011.

Question 5

A city claims that 75% of all low income housing is 1500 sq.ft.The tenants believe the proportion of housing this size is smaller than the claim,and hire an independent firm to test a random sample size of 120 and found 1500 sq.ft.housing at 66%.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

A) $\mathrm { H } _ { 0 }$ : p = 0.75; $\mathrm { H } _ { \mathrm { A } }$ : p ? 0.75; z = -2.32; P-value = 0.0204.This data shows strong evidence that the proportion of 1500 sq.ft.housing is less than 75%.
B) $\mathrm { H } _ { 0 }$ : p = 0.75; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.075 z = 2.28; P-value = 0.0113.This data shows weak evidence that the proportion of 1500 sq.ft.housing is less than 75%.
C) $\mathrm { H } _ { 0 }$ : p = 0.75; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.75; z = -2.32; P-value = 0.9898.This data shows no evidence that the proportion of 1500 sq.ft.housing is less than 75%.
D) $\mathrm { H } _ { 0 }$ : p = 0.75; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.75; z = 2.32; P-value = 0.9898.This data shows strong evidence that the proportion of 1500 sq.ft.housing is less than 75%.
E) $\mathrm { H } _ { 0 }$ : p = 0.75; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.75; z = -2.28; P-value = 0.0113.This data shows strong evidence that the proportion of 1500 sq.ft.housing is less than 75%.

Question 6

Census data for a certain city shows that 22% of residents are European.Suppose 94 people are called for jury duty,and only 15 of them are European.Does this call into question the fairness of the jury selection system? Use a calculator to find z-scores and P-values.

Question 7

During the 2004 season,home teams in the same conference won 189 out of 302 regular season college basketball games.Test the home team advantage hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Question 8

What is the general statement in the null hypothesis in a One-Sample hypothesis test?

A)Parameter = Estimate
B)Parameter = Hypothesized Value
C)Estimate = Hypothesized Value
D)Statistic = Estimate
E)Parameter = Alternative Value

Question 9

A university wants to increase its retention rate of 4% for graduating students from the previous year.After implementing several new programs during the last two years,the university reevaluated its retention rate using a random sample of 352 students and found the retention rate at 5%.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

A) $\mathrm { H } _ { 0 }$ : p = 0.04; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.04; z = 0.96; P-value = 0.1685.This data shows virtually no evidence that more than 4% of students are retained; the university should not continue with the new programs.
B) $\mathrm { H } _ { 0 }$ : p = 0.04; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.04; z = 1.07; P-value = 0.8577.This data shows conclusive evidence that more than 4% of students are retained; therefore,the university should continue with the new programs.
C) $\mathrm { H } _ { 0 }$ : p = 0.04; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.04; z = -1.07; P-value = 0.8577.This data shows conclusive evidence that more than 4% of students are retained; the university should continue with the new programs.
D) $\mathrm { H } _ { 0 }$ : p = 0.04; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.04; z = -1.07; P-value = 0.1423.This data does not show that more than 4% of students are retained; the university should not continue with the new programs.
E) $\mathrm { H } _ { 0 }$ : p = 0.04; $\mathrm { H } _ { \mathrm { A } }$ : p ? 0.04; z = 1.07; P-value = 0.2846.This data shows virtually no evidence that more than 4% of students are retained; the university should not continue with the new programs.

Question 10

A mayor is concerned about the percentage of city residents who express disapproval of his job performance.His political committee pays for a newspaper ad,hoping that it will keep the disapproval rate below 21%.They will use a follow-up poll to assess the ad's effectiveness.

A)H0: p > 0.21 HA: p < 0.21
B)H0: p > 0.21 HA: p = 0.21
C)H0: p < 0.21 HA: p = 0.21
D)H0: p = 0.21 HA: p > 0.21
E)H0: p = 0.21 HA: p < 0.21

Question 11

Five years ago,a company found that 8% of its employees commuted to work by car.A survey investigates whether the current proportion of employees who commute by car to work is higher than it was five years ago.A test on employee commuting by car was done on a random sample of 1000 employees,and found car commuting to be 12%.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

A) $\mathrm { H } _ { 0 }$ : p = 0.08; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.08; z = 4.66; P-value < 0.00001.This data shows conclusive evidence that the proportion in car commuting is greater than 8%.
B) $\mathrm { H } _ { 0 }$ : p = 0.08; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.08; z = -4.66; P-value > 0.00001.This data shows conclusive evidence that the proportion in car commuting is greater than 8%.
C) $\mathrm { H } _ { 0 }$ : p = 0.08; $\mathrm { H } _ { \mathrm { A } }$ : p ? 0.08; z = 4.66; P-value < 0.99999.This data shows no evidence that the proportion in car commuting is greater than 8%.
D) $\mathrm { H } _ { 0 }$ : p = 0.08; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.08; z = 4.66; P-value < 0.99999.This data shows no evidence that the proportion in car commuting is greater than 8%.
E) $\mathrm { H } _ { 0 }$ : p = 0.08; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.08; z = -4.66; P-value > 0.99999.This data shows no evidence that the proportion in car commuting is greater than 8%.

Question 12

An airline's public relations department says that the airline rarely loses passengers' luggage.It further claims that on those occasions when luggage is lost,92% is recovered and delivered to its owner within 24 hours.A consumer group who surveyed a large number of air travelers found that only 145 out of 165 people who lost luggage on that airline were reunited with the missing items by the next day.Does this cast doubt on the airline's claim? Use a calculator to find z-scores and P-values.

Question 13

A new manager,hired at a large warehouse,was told to reduce the 26% employee sick leave.The manager introduced a new incentive program for employees with perfect attendance.The manager decides to test the new program to see if it's better.What are the null and alternative hypotheses?

A)H0: p < 0.26 HA: p = 0.26
B)H0: p = 0.26 HA: p > 0.26
C)H0: p = 0.26 HA: p < 0.26
D)H0: p > 0.26 HA: p < 0.26
E)H0: p = 0.26 HA: p ≠ 0.26

Question 14

What is the general statement in the null hypothesis in a One-Sample hypothesis test?

A)Parameter = Alternative Value
B)Parameter ≠ Hypothesized Value
C)Parameter > Hypothesized Value
D)Parameter < Hypothesized Value
E)Parameter = Hypothesized Value

Question 15

A newspaper is considering the launch of an online edition.The newspaper plans to go ahead only if it's convinced that more than 35% of current readers would subscribe.The newspaper contacts a simple random sample of 1000 current subscribers,and 345 of those surveyed expressed interest.What should the company do? Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.Use a calculator to find z-scores and P-values.

Question 16

A weight loss centre provided a loss for 72% of its participants.The centre's leader decides to test a new weight loss strategy on a random sample size of 140 and found weight loss in 78% of the participants.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

A) $\mathrm { H } _ { 0 }$ : p = 0.72; $\mathrm { H } _ { \mathrm { A } }$ : p ? 0.72; z = 1.58; P-value = 0.1236.This data shows weak evidence of a weight loss in more than 72% of the participants in the weight loss strategy; the manager should not continue with this strategy.
B) $\mathrm { H } _ { 0 }$ : p = 0.72; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.72; z = 1.58; P-value = 0.0571.This data shows moderate evidence of a weight loss in more than 72% of the participants in the weight loss strategy; it is hard to say whether or not they should use this strategy,perhaps further testing is in order.
C) $\mathrm { H } _ { 0 }$ : p = 0.72; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.72; z = -1.58; P-value = 0.0618.This data shows weak evidence of a weight loss in more than 72% of the participants in the weight loss strategy; the manager should change strategies.
D) $\mathrm { H } _ { 0 }$ : p = 0.72; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.72; z = -1.58; P-value = 0.9382.This data shows conclusive evidence of a weight loss in more than 72% of the participants in the weight loss strategy; the manager should continue with this strategy.
E) $\mathrm { H } _ { 0 }$ : p = 0.72; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.72; z = 1.58; P-value = 0.9382.This data shows conclusive evidence of a weight loss in more than 72% of the participants in the weight loss strategy; the manager should continue with this strategy.

Question 17

4% of trucks of a certain model have needed new engines after being driven between 0 and 100 kilometres.The manufacturer hopes that the redesign of one of the engine's components has solved this problem.

A)H0: p < 0.04 HA: p = 0.04
B)H0: p > 0.04 HA: p = 0.04
C)H0: p < 0.04 HA: p > 0.04
D)H0: p = 0.04 HA: p < 0.04
E)H0: p = 0.04 HA: p > 0.04

Question 18

At a local university,only 62% of the original freshman class graduated in four years.Has this percentage changed?

A)H0: p ≠ 0.62 HA: p = 0.62
B)H0: p < 0.62 HA: p > 0.62
C)H0: p < 0.62 HA: p = 0.62
D)H0: p = 0.62 HA: p ≠ 0.62
E)H0: p = 0.62 HA: p < 0.62

Question 19

A weight loss centre provided a loss for 72% of its participants.The centre's leader decides to test a new weight loss strategy to see if it's better.What are the null and alternative hypotheses?

A)H0: p = 0.72 HA: p > 0.72
B)H0: p > 0.72 HA: p < 0.72
C)H0: p = 0.72 HA: p ≠ 0.72
D)H0: p = 0.72 HA: p < 0.72
E)H0: p > 0.72 HA: p = 0.72

Question 20

Which conditional probability statement below best describes the P-Value?

A)P(H0 is true | Data).
B)P(Data | HA is true).
C)P(HA is true | Data).
D)P(Data | H0 is true).
E)P(H0 is true |HA is false).

Question 21

In 2010,the proportion of employees at a large company who commuted to work by car was 8%.A current survey investigates whether the proportion of employees who commute by car to work is higher than it was in 2010.What are the null and alternative hypotheses?

A)H0: p = 0.08 HA: p < 0.08
B)H0: p > 0.08 HA: p < 0.08
C)H0: p = 0.08 HA: p > 0.08
D)H0: p = 0.08 HA: p ≠ 0.08
E)H0: p < 0.08 HA: p = 0.08

Question 22

Suzie has installed a new spam blocker program on her email.She used to receive an average of 20 spam emails a day.Is the new program working?

A) $\mathrm { H } _ { 0 }$ : ? = 20 $\mathrm { H } _ { \mathrm { A } }$ : ? < 20
B) $\mathrm { H } _ { 0 }$ : ? = 20 $\mathrm { H } _ { \mathrm { A } }$ : ? ? 20
C) $\mathrm { H } _ { 0 }$ : ? = 20 $\mathrm { H } _ { \mathrm { A } }$ : ? > 20
D) $\mathrm { H } _ { 0 }$ : ? > 20 $\mathrm { H } _ { \mathrm { A } }$ : ? = 20
E)Not enough information is given.

Question 23

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose we claim that the current unemployment rate differs from the April 2011 unemployment rate.If we wish to support our claim,what are the null and alternative hypotheses?

A)H0: p = 0.076 HA: p ≠ 0.076
B)H0: p = 0.076 HA: p > 0.076
C)H0: p > 0.076 HA: p < 0.076
D)H0: p < 0.076 HA: p = 0.076
E)H0: p ≠ 0.076 HA: p = 0.076

Question 24

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Statistics Canada claims that the current unemployment rate is lower than that of April 2011.To test this claim,a hypothesis test is conducted and yields a P-value turns out to be 0.04.Provide an appropriate conclusion.

A)If the current unemployment rate is 7.6%,there is a 4% chance of seeing a sample unemployment rate as low (or lower)than what we observed from natural sampling variation.There is no evidence of that the unemployment rate decreased,but we cannot conclude there is no change in the unemployment rate.
B)There is a 4% chance of no change in the unemployment rate.
C)There is a 96% chance of no change in the unemployment rate.
D)We can say there is a 4% chance of seeing a change in the unemployment rate in the results we observed from natural sampling variation.We conclude that Statistics Canada is correct and the unemployment rate has decreased.
E)If the current unemployment rate is 7.6%,there is a 4% chance of seeing a sample unemployment rate as low (or lower)than what we observed from natural sampling variation.There is strong evidence that Statistics Canada is correct and the unemployment rate has decreased.

Question 25

The management of a water park has concerns about the chlorine level of 0.4% mg/mL increasing to an unsafe level.The management tests the hypothesis that the park's chlorine proportions have remained the same,and find a P-value of 0.005.Provide an appropriate conclusion

A)There is a 99.5% chance of no change in the chlorine proportion.
B)We can say there is a 0.5% chance of seeing a change in the chlorine proportions in the results we observed from natural sampling variation.We conclude the chlorine proportion is higher.
C)There is a 0.5% chance of no change in the chlorine proportion.
D)If the chlorine level is 0.4% mg/mL,then there is a 0.5% chance of seeing a sample chlorine level as high (or higher)than what we observed from natural sampling variation.There is no evidence of a higher chlorine proportion,but we cannot conclude the chlorine proportion is the same.
E)If the chlorine level is 0.4% mg/mL,then there is a 0.5% chance of seeing a sample chlorine level as high (or higher)than what we observed from natural sampling variation.There is very strong evidence the chlorine proportion is higher.

Question 26

According to the 2004 Canadian Community Health Survey,23.1% of Canadians aged 18 or older were considered obese; that is,they had a body mass index (BMI)of 30 or higher.Suppose you believe that the percentage of obese Canadians has increased since 2004 and wish to test your belief.Based on a 2014 survey,you conduct a hypothesis test and come up with a P-value of 0.028.What is reasonable to conclude?

A)If the percentage of obese Canadians has not changed,then there is a 2.8% chance of seeing the increase in the percentage of obese Canadians that we observed (or higher)from natural sampling variation.There is no evidence the percentage of obese Canadians has increased since 2004,but we cannot conclude the percentage hasn't increased.
B)There is a 97.2% chance that the percentage of obese Canadians has increased since 2004.
C)There is a 2.8% chance that the percentage of obese Canadians has increased since 2004.
D)If the percentage of obese Canadians has not changed,then there is a 2.8% chance of seeing the increase in the percentage of obese Canadians that we observed (or higher)from natural sampling variation.There is strong evidence that the percentage of obese Canadians has increased since 2004.
E)We can say there is a 2.8% chance that the percentage of obese Canadians has increased in the results we observed from natural sampling variation.We conclude that the percentage of obese Canadians has not increased since 2004.

Question 27

You want to see if the number of minutes cell phone users use each month has changed from its mean of 120 minutes 2 years ago.You take a random sample of 100 cell phone users and find an average of 135 minutes used.

A) $\mathrm { H } _ { 0 }$ : ? = 120 $\mathrm { H } _ { \mathrm { A } }$ : ? > 120
B) $\mathrm { H } _ { 0 }$ : ? = 135 $\mathrm { H } _ { \mathrm { A } }$ : ? > 135
C) $\mathrm { H } _ { 0 }$ : ? = 120 $\mathrm { H } _ { \mathrm { A } }$ : ? < 120
D) $\mathrm { H } _ { 0 }$ : ? = 135 $\mathrm { H } _ { \mathrm { A } }$ : ? ? 135
E) $\mathrm { H } _ { 0 }$ : ? = 120 $\mathrm { H } _ { \mathrm { A } }$ : ? ? 120

Question 28

After a political ad campaign for a city's mayor,pollsters check the disapproval ratings.They test the hypothesis that the ads produced no change against the alternative that the ratings are now below 19%,and find a P-value of 0.17.Provide an appropriate conclusion.

Question 29

A weight loss program provided a loss for 60% of its participants.The program leader decides to test a new weight loss strategy to see if it's better and gets a P-value of 0.21.Is it reasonable to conclude that the new strategy and the old one are equally effective?

Question 30

Are Canadians getting fatter? Researchers interested in this question take a random sample of 500 people and record an average weight of 86 kg.Ten years ago,the average weight was 83 kg.

A) $\mathrm { H } _ { 0 }$ : ? = 86 $\mathrm { H } _ { \mathrm { A } }$ : ? < 86
B) $\mathrm { H } _ { 0 }$ : ? = 83 $\mathrm { H } _ { \mathrm { A } }$ : ? > 83
C) $\mathrm { H } _ { 0 }$ : ? = 86 $\mathrm { H } _ { \mathrm { A } }$ : ? > 86
D) $\mathrm { H } _ { 0 }$ : ? = 83 $\mathrm { H } _ { \mathrm { A } }$ : ? < 83
E) $\mathrm { H } _ { 0 }$ : ? = 83 $\mathrm { H } _ { \mathrm { A } }$ : ? ? 83

Question 31

A university wants to increase its retention rate of 4% for graduating students from the previous year.After implementing several new programs during the last two years,the university reevaluates its retention rate and comes up with a P-value of 0.075.What is reasonable to conclude about the new programs?

A)There is a 7.5% chance of the new programs having no effect on retention.
B)If the new programs have no effect on the retention rate,then there is a 7.5% chance of seeing the increase in the retention rate that we observed (or higher)from natural sampling variation.We conclude the new programs are more effective.
C)If the new programs have no effect on the retention rate,then there is a 7.5% chance of seeing the increase in the retention rate that we observed (or higher)from natural sampling variation.There is suggestive but inconclusive evidence the new programs are more effective,but we cannot conclude the new programs have no effect on retention.
D)We can say there is a 7.5% chance of seeing the new programs having an effect on retention in the results we observed from natural sampling variation.We conclude the new programs are more effective.
E)There is a 92.5% chance of the new programs having no effect on retention.

Question 32

A city claims that 75% of all low income housing is 1500 sq.ft.The tenants believe the proportion of housing this size is smaller than the claim,and hire an independent firm to test an appropriate hypothesis.What are the null and alternative hypotheses?

A)H0: p > 0.75 HA: p < 0.75
B)H0: p < 0.75 HA: p = 0.75
C)H0: p = 0.75 HA: p < 0.75
D)H0: p = 0.75 HA: p > 0.75
E)H0: p = 0.75 HA: p ≠ 0.75

Question 33

A survey investigation whether the proportion of employees who commute by car to work is higher than it was five years ago finds a P-value of 0.009.Is it reasonable to conclude that more employees are commuting by car?

Question 34

Health Canada reports that,in 2007,85.7% of Canadians were satisfied with the health care services they received.Suppose you are now concerned that a smaller percentage of Canadians are satisfied with the health care services they received.If you want to justify your concerns,what are the null and alternative hypotheses?

A)H0: p < 0.857 HA: p = 0.857
B)H0: p = 0.857 HA: p > 0.857
C)H0: p = 0.857 HA: p < 0.857
D)H0: p > 0.857 HA: p = 0.857
E)H0: p = 0.857 HA: p ≠ 0.857

Question 35

The seller of a loaded die claims that it will favor the outcome 6.We don't believe that claim,and roll the die 350 times to test an appropriate hypothesis.Our P-value turns out to be 0.01.Provide an appropriate conclusion.

Question 36

A new manager,hired at a large warehouse,was told to reduce the 26% employee sick leave.The manager introduced a new incentive program for employees with perfect attendance.The manager decides to test the new program to see if it's better and receives a P-value of 0.06.What is reasonable to conclude about the new strategy?

A)There is a 94% chance of the new program having no effect on employee attendance.
B)If the sick leave percentage has not changed,then there is a 6% chance of seeing the decrease in the sick leave percentage we observed (or lower)from natural sampling variation.We can conclude the new program is more effective.
C)There is a 6% chance of the new program having no effect on employee attendance.
D)We can say there is a 6% chance of seeing the new program having no effect on employee attendance in the results we observed from natural sampling variation.We conclude the new program is more effective.
E)If the sick leave percentage has not changed,then there is a 6% chance of seeing the decrease in the sick leave percentage we observed (or lower)from natural sampling variation.There is moderate evidence the new program is more effective,but we cannot conclude the program has no effect on employee attendance.

Question 37

Has the introduction of more music download services changed the number of university students downloading music online without paying for it? Two years ago,approximately 50,000 college students admitted to downloading music online without paying for it.

A) $\mathrm { H } _ { 0 }$ : ? < 50,000 $\mathrm { H } _ { \mathrm { A } }$ : ? = 50,000
B) $\mathrm { H } _ { 0 }$ : ? = 50,000 $\mathrm { H } _ { \mathrm { A } }$ : ? > 50,000
C) $\mathrm { H } _ { 0 }$ : ? = 50,000 $\mathrm { H } _ { \mathrm { A } }$ : ? < 50,000
D) $\mathrm { H } _ { 0 }$ : ? = 50,000 $\mathrm { H } _ { \mathrm { A } }$ : ? ? 50,000
E) $\mathrm { H } _ { 0 }$ : ? > 50,000 $\mathrm { H } _ { \mathrm { A } }$ : ? = 50,000

Question 38

A city claims that 75% of all low income housing is 1500 sq.ft.The tenants believe the proportion of housing this size is smaller than the claim,and hire an independent firm to test an appropriate hypothesis.The P-value turns out to be 0.025.Provide an appropriate conclusion.

A)There is a 2.5% chance of no change in the proportion of housing that is 1500 sq.ft.
B)There is a 97.5% chance of no change in the proportion of housing that is 1500 sq.ft.
C)We can say there is a 2.5% chance of seeing a change in the proportion of housing that is 1500 sq.ft.in the results we observed from natural sampling variation.We conclude the tenants are correct and that the proportion of housing with 1500 square feet is less than 75%.
D)If 75% of all low income housing is 1500 sq.ft.,then there is a 2.5% chance of seeing a sample proportion of such houses as low (or lower)than what we observed from natural sampling variation.There is no evidence of that the proportion of housing is smaller than 1500 sq.ft.,but we cannot conclude there is no change in the proportion of housing that is 1500 sq.ft.
E)If 75% of all low income housing is 1500 sq.ft.,then there is a 2.5% chance of seeing a sample proportion of such houses as low (or lower)than what we observed from natural sampling variation.There is strong evidence the tenants are correct and that the proportion of housing with 1500 square feet is less than 75%.

Question 39

You are considering moving to Richmond Hill and are concerned about the average one-way commute time to downtown Toronto.Does the average one-way commute time exceed 25 minutes? You take a random sample of 100 Richmond Hill residents and find an average commute time of 29 minutes with a standard deviation of 7 minutes.

A) $\mathrm { H } _ { 0 }$ : ? = 25 $\mathrm { H } _ { \mathrm { A } }$ : ? < 25
B) $\mathrm { H } _ { 0 }$ : ? = 25 $\mathrm { H } _ { \mathrm { A } }$ : ? > 25
C) $\mathrm { H } _ { 0 }$ : ? = 29 $\mathrm { H } _ { \mathrm { A } }$ : ? < 29
D) $\mathrm { H } _ { 0 }$ : ? = 25 $\mathrm { H } _ { \mathrm { A } }$ : ? ? 25
E) $\mathrm { H } _ { 0 }$ : ? = 29 $\mathrm { H } _ { \mathrm { A } }$ : ? > 29

Question 40

Is the mean weight of female college students equal to 59 kg? To test this,you take a random sample of 80 students,finding a mean of 61 kg with a standard deviation of 8.4 kg.

A)Fail to reject the null hypothesis of μ = 59 with a P-value of 0.9668.There is not sufficient evidence that the weight of female students has changed.
B)Fail to reject the null hypothesis of μ = 59 with a P-value of 0.0166.There is not sufficient evidence that the weight of female students has changed.
C)Reject the null hypothesis of μ = 59 with a P-value of 0.0332.There is sufficient evidence that the weight of female students has changed.
D)Reject the null hypothesis of μ = 59 with a P-value of 0.0166.There is sufficient evidence that the weight of female students has changed.
E)There is not enough information to perform the test.

Question 41

A test of sobriety involves measuring the subject's motor skills.Sixty-four randomly selected sober subjects take the test and produce a mean score of 41.0 with a standard deviation of 3.4.Test the claim that the true mean score for all sober subjects is equal to 40.5.

A)Fail to reject the null hypothesis of μ = 40.5 with a P-value of 0.0265.There is not sufficient evidence that the true mean score for sober subjects is different from 40.5.
B)Reject the null hypothesis of μ = 40.5 with a P-value of 0.0165.There is sufficient evidence that the true mean score for sober subjects is different from 40.5.
C)Reject the null hypothesis of μ = 40.5 with a P-value of 0.1190.There is strong evidence that the true mean score for sober subjects is not 40.5.
D)Fail to reject the null hypothesis of μ = 40.5 with a P-value of 0.2380.There is not sufficient evidence that the true mean score for sober subjects is different from 40.5.
E)There is not enough information to perform the test.

Question 42

Is the mean lifetime of particular type of car engine greater than 350,000 km? To test this claim,a sample of 100 engines is measured,yielding an average of 354,585 km and a standard deviation of 18515 km.

A)Reject the null hypothesis of μ = 350,000 with a P-value of 0.0134.There is sufficient evidence that the mean engine lifetime is longer than 350,000 km.
B)Reject the null hypothesis of μ = 350,000 with a P-value of 0.0066.There is sufficient evidence that the mean engine lifetime is longer than 350,000 km.
C)Fail to reject the null hypothesis of μ = 350,000 with a P-value of 0.9934.There is not sufficient evidence that the mean engine lifetime is longer than 350,000 km.
D)Fail to reject the null hypothesis with a P-value of 0.0735.There is not sufficient evidence that the mean engine lifetime is longer than 350,000 km.
E)There is not enough information to perform the test.

Question 43

A large software company gives job applicants a test of programming ability,and the mean for the test has been 160 in the past.One-hundred applicants are randomly selected from one large university and they produce a mean score of 163,with a standard deviation of 13.Is there enough evidence to indicate that the sample comes from a population with a mean score greater than 160?

A)No.With a P-value of 0.9896,we fail to reject the null hypothesis of μ = 160.
B)Yes.With a P-value of 0.0208,we reject the null hypothesis of μ = 160.
C)Yes.With a P-value of 0.0104,we reject the null hypothesis of μ = 160.
D)No.With a P-value of 0.9792,we fail to reject the null hypothesis of μ = 160.
E)There is not enough information to perform the test.

Question 44

Marc wants to know if the mean age of the employees at his company is less than 26 years.He obtains a random sample of 100 employees,and finds a mean age of 25.1 years and a standard deviation of 9.2 years.

A)Fail to reject the null hypothesis of μ = 26 with a P-value of 0.1635.There is not sufficient evidence that the mean age is less than 26 years.
B)Reject the null hypothesis of μ = 26 with a P-value of 0.0425.The evidence suggests that the mean age is less than 26 years.
C)Fail to reject the null hypothesis of μ = 26 with a P-value of 0.8365.There is not sufficient evidence that the mean age is less than 26 years.
D)Reject the null hypothesis of μ = 26 with a P-value of 0.018.There is sufficient evidence that the mean age is less than 26 years.
E)There is not enough information to perform the test.