Consider the following hypothesis test: H 0 : 25 H a : > 25 A sample of 40 provi

Question

Consider the following hypothesis test:

H0: 25
Ha: > 25

A sample of 40 provided a sample mean of 26.4. The population standard deviation is 5.

a. Compute the value of the test statistic (to 2 decimals).

b. What is the p-value (to 4 decimals)?

c. At = .01, what is your conclusion?

P-value is:

A) Greater than or equal to 0.01, reject H0

B) Greater than 0.01, do not reject H0

C) Less than or equal to 0.01, do not reject H0

D) Less than 0.01, reject H0

E) Equal to 0.01, do not reject H0

F) Not Equal to 0.01, do not reject H0

d. What is the rejection rule using the critical value?

Reject H0 if z is

A) Greater than or equal to 2. 33

B) Greater than 2.33

C) Less than or equal to 2.33

D) Less than 2.33

E) Equal to 2.33

F) Not equal to 2.33

What is your conclussion?

What is your conclusion? The test statistic is greater than or equal to the critical value. Do not reject.Ho Select The test statistic is greater than or equal to the critical value. Do not reject. The test statistic is less than the critical value. Reject. The test statistic is greater than the critical value. Do not reject. The test statistic is less than the critical value. Do not reject. The test statistic is equal to the critical value. Reject. The test statistic is not equal to the critical value. Do not reject.

Explanation / Answer

The statistical software output for this problem is:

One sample Z summary hypothesis test:
: Mean of population
H0 : = 25
HA : > 25
Standard deviation = 5

Hypothesis test results:

Hence,

Test statistic = 1.77

P - value = 0.0383

P - value is Greater than 0.01, do not reject H0. Option B is correct.

Reject Ho if z is Greater than 2.33. Option B is correct.

Conclusion: The test statistic is less than the critical value. Do not reject. Option D is correct.

Mean n Sample Mean Std. Err. Z-Stat P-value 40 26.4 0.79056942 1.7708755 0.0383

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