Question 1

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.

Accepted Answer

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 2

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.

Accepted Answer

The answer of The seller of a loaded die claims...

Question 3

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.

Accepted Answer

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 4

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.

Accepted Answer

A)  $\mathrm { H } _ { 0 }$ : ?  50,000 
C)  $\mathrm { H } _ { 0 }$ : ? = 50,000 $\mathrm { H } _ { \mathrm { A } }$ : ?  50,000 $\mathrm { H } _ { \mathrm { A } }$ : ? = 50,000

Question 5

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

Accepted Answer

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

Question 6

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.

Accepted Answer

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 = 0.9633.This data shows strong evidence that the unemployment rate has decreased since April of 2011.

Question 7

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.

Accepted Answer

A)  $\mathrm { H } _ { 0 }$ : p = 0.08; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.08; z = 4.66; P-value  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%.

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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.

Question 10

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

Accepted Answer

Question 11

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?

Accepted Answer

A) H0: p = 0.231 HA: p  0.231 
E) H0: p  0.231

Question 12

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?

Accepted Answer

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 13

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.

Accepted Answer

The answer of During the 2004 season,home teams in the...

Question 14

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?

Accepted Answer

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 15

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?

Accepted Answer

A) H0: p = 0.08 HA: 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 16

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.

Accepted Answer

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 17

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.

Accepted Answer

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

Question 18

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?

Accepted Answer

A) H0: p  0.857 
C) H0: p = 0.857 HA: p  0.857 HA: p = 0.857 
E) H0: p = 0.857 HA: p ≠ 0.857

Question 19

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.

Accepted Answer

A)  $\mathrm { H } _ { 0 }$ : 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.

Question 20

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.

Accepted Answer

The answer of A newspaper is considering the launch of...

Exam 17: Testing Hypotheses About Proportions

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.

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.

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.

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

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

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

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

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?

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.

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?

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 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.