Question 1

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) 
B) 
C) 
D) 
E)

Accepted Answer

We can use a one-sample t-test with a significance level of 0.05 to test whether the average commute time for Richmond Hill residents is significantly higher than 25 minutes. The null hypothesis is that the true population mean commute time is equal to 25 minutes, and the alternative hypothesis is that it is greater than 25 minutes.

Using the sample data, we calculate the t-statistic as (29-25)/(7/sqrt(100)) = 4.57. The degrees of freedom are n-1 = 99. Checking the t-distribution table with 99 degrees of freedom at a significance level of 0.05, the critical value is 1.660.

Since our calculated t-statistic (4.57) is greater than the critical value (1.660), we reject the null hypothesis and conclude that the average one-way commute time in Richmond Hill is significantly greater than 25 minutes. Therefore, choice B is the best answer.

Question 2

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) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of You want to see if the number...

Question 3

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.

Accepted Answer

Given the information, the correct choice is to fail to reject the null hypothesis with a P-value of 0.1635, indicating insufficient evidence to conclude that the mean age is less than 26 years.

Question 4

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.

Accepted Answer

The answer of Is the mean weight of female college...

Question 5

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) 
B) 
C) 
D)

E) Not enough information is given.

Accepted Answer

The answer of Suzie has installed a new spam blocker...

Question 6

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.

Accepted Answer

We need to perform a one-sample t-test with the null hypothesis that the mean lifetime is 350,000 km and the alternative hypothesis that the mean lifetime is greater than 350,000 km. With a sample size of 100, the degrees of freedom are 99. Using a t-distribution table or calculator, a t-value of 2.468 is found with a one-tailed test and α = 0.05. The calculated t-value for this sample is (354,585 - 350,000)/(18515/√100) = 2.46. This calculated t-value is greater than the critical t-value, and the corresponding p-value is 0.0066, which is less than α. Therefore, we reject the null hypothesis and conclude that there is sufficient evidence that the mean engine lifetime is longer than 350,000 km.

Question 7

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.

Accepted Answer

The answer of A test of sobriety involves measuring the...

Question 8

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) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Has the introduction of more music download...

Question 9

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.

Accepted Answer

The answer of A large software company gives job applicants...

Question 10

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) 
B) 
C) 
D) 
E)

Accepted Answer

The sample size is sufficiently large (n=500) to make meaningful conclusions about the population. The difference between the current average weight (86 kg) and the average weight 10 years ago (83 kg) suggests that Canadians may be getting heavier. However, further analysis (such as hypothesis testing) would be needed to confirm whether this difference is statistically significant. Therefore, B is the best choice as it acknowledges the potential trend but does not make any definitive conclusions.

Quiz 19: Testing Hypotheses About Proportions

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.

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.

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.

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?

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 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.

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.

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.