Question

AT&T would like to test the hypothesis that the average revenue per retail user for Verizon Wireless customers is greater than $50. A random sample of 32 Verizon Wireless customers provided an average revenue of $54.70. It is believed that the population standard deviation for the revenue per retail user is $11.00. Using LaTeX: \alpha=0.05α = 0.05 , answer the following questions: a. Identify the null and alternative hypotheses to conduct an appropriate hypothesis test of mean. (3 points) b. Use the critical value approach to test this hypothesis. (3 points) State your decision and conclusions explicitly. (3 points) c. Use the p-value approach to test this hypothesis. (3 points) State your decision and conclusions explicitly. (3 points) d. Assume that the actual population mean for revenue per retail user is $44.30. Calculate the probability of type II error. (5 points)

Answer 1

H0; u = 50 average revenue equals 50

H1: u not equal to 50, average revenue not equal to 50

This is 2 tailed

Alpha = 0.05

Z critical = 1.6449

We find the test statistics

Mean = 54.7

Sd = 11

n = 32

barX - u/sd/√n

= 54.70-50/11/√32

= 4.70/1.9435

= 2.418

Decision rule: reject H0 if test statistic > critical value. Accept if otherwise

2.418>1.6449

We reject H0

We conclude that average revenue is not equal to zero

C. P(z>=2.418) = 0.9922

1 - 0.9922

= 0.0078 (I used Ms excel here)

0.0078 < 0.05

So we Reject h0