A) calculate the value of ththe test statistic, set up. the rejection region, deermine the P- value, interpret the result and draw the sampling distribution

H0: = 50

H1: < 50

= 15 n=100 xbar= 48 a=.05

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. 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?