Question

A "sleep habits" survey answered by 46 randomly selected New Yorkers contained the question "How much sleep do you get per night?" The sample average was 7.8 hours, with a corresponding sample standard deviation of 0.82 hours. We want to test against the null hypothesis that New Yorkers get, on average, 8 hours of sleep per night. α=0.05.

a. This null hypothesis should be formally written as: (You have two attempts at this question.)

H0: μdifference = 8

H0: μ = 0 H0: μ = 8

H0: μ1 - μ2 = 0

H0: μdifference = 0

H0: μ1 - μ2 = 8

b. The t test statistic is: Round your answer to 3 decimal places

c. The approximate 95% CI is: to Round your answer to 3 decimal places

d. The statistical decision and its justification are: (You have two attempts at this question.)

|Test statistic| < 2 and 95% CI does not contain null value, so reject H0 |Test statistic| < 2 and 95% CI contains null value, so reject H0

|Test statistic| > 2 and 95% CI does not contain null value, so reject H0

|Test statistic| > 2 and 95% CI contains null value, so reject H0

|Test statistic| < 2 and 95% CI does not contain null value, so fail to reject H0

|Test statistic| < 2 and 95% CI contains null value, so fail to reject H0

|Test statistic| > 2 and 95% CI does not contain null value, so fail to reject H0

|Test statistic| > 2 and 95% CI contains null value, so fail to reject H0

e. It is possible that the statistical decision from part d. is an error. What type of error could it possibly be, and why? (You have two attempts at this question.)

This could be a Type I error, because, despite our decision, the null hypothesis might actually be true.

This could be a Type I error, because, despite our decision, the null hypothesis might actually be false.

This could be a Type I error, because, despite our decision, the null hypothesis might actually be rejected.

This could be a Type I error, because, despite our decision, the null hypothesis might actually fail to be rejected.

This could be a Type II error, because, despite our decision, the null hypothesis might actually be true.

This could be a Type II error, because, despite our decision, the null hypothesis might actually be false.

This could be a Type II error, because, despite our decision, the null hypothesis might actually be rejected.

This could be a Type II error, because, despite our decision, the null hypothesis might actually fail to be rejected.

Answer 1

a)

b)The t test statistic is

c)

d)|Test statistic| < 2 it is then concluded that the null hypothesis is not rejected.

95% CI contains null value, so fail to reject H0

e)Since we donot reject the null hypothesis. This could be a Type II error, because, despite our decision, the null hypothesis might actually be false.