Question 1

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 2

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 can use a one-sample t-test to test this claim. The null hypothesis is that the true mean lifetime of the engine is 350,000 km and the alternative hypothesis is that the true mean is greater than 350,000 km.

The test statistic is calculated as:

t = (x̄ - μ) / (s / √n) = (354,585 - 350,000) / (18515 / √100) = 2.47

Where x̄ is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Using a t-distribution with 99 degrees of freedom (100-1), the p-value for this test is 0.0066 (calculated using a two-tailed test, and doubling the p-value since this is a one-tailed test).

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis. Therefore, there is sufficient evidence that the mean engine lifetime is longer than 350,000 km. The correct answer is B.

Question 3

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 4

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.

Quiz 17: Testing Hypotheses About Proportions

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.

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.

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.