A) a. Compute thep-value in order to test the following hypotheses given that= 52,n= 9, and = 5.

H0: = 50

H1: > 50

b. Repeat part (a) withn= 25.

c. Repeat part (a) withn= 100.

d. Describe what happens to the value of the test statistic and its p-value when the sample size increases.

B) a. A statistics practitioner formulated the following hypotheses.

H0: = 200

H1: <200

and learned that= 190,n= 9, and = 50

Compute the p-value of the test.

b. Repeat part (a) with = 30.

c. Repeat part (a) with = 10

d. Discuss what happens to the value of the test statistic and itsp-value when the standard deviation decreases.

C) a. Given the following hypotheses, determine thep-value when= 21,n= 25, and = 5.

H0: = 20

H1: 20

b. Repeat part (a) with x = 22.

c. Repeat part (a) with x = 23.

d. Describe what happens to the value of the test statistic and itsp-value when the value ofincreases.

D) a. Test these hypotheses by calculating the p-value given that= 99,n= 100, and = 8

H0: = 100

H1: 100

b. Repeat part (a) with n = 50.

c. Repeat part (a) with n = 20.

d. What is the effect on the value of the test statistic and thep-value of the test when the sample size decreases?

E) a. Find the p-value of the following test given that= 990,n= 100, and = 25.

H0: = 1000

H1: <1000

b. Repeat part (a) with = 50.

c. Repeat part (a) with = 100.

d. Describe what happens to the value of the test statistic and itsp-value when the standard deviation

F) a. Calculate the p-value of the test described here.

H0: = 60

H1: > 60

= 72,n= 25, = 20

b. Repeat part (a) with x = 68.

c. Repeat part (a) with x = 64.

d. Describe the effect on the test statistic and thep-value of the test when the value ofdecreases.