A movie theater manager believes the average number of times a customer goes to

Question

A movie theater manager believes the average number of times a customer goes to a movie in a year is at least 24. To test his claim, the theater employees conduct a poll of 25 randomly selected customers and get a sample mean of 25.1 with a sample standard deviation of 7.9. What is the Null Hypothesis and the Alternative Hypothesis? Assuming the population is normal, should we use the Normal z-test or the Student's t-test? If we use a 0.05 significance level, what is the critical value for the test? What is the value of the test statistic? Should we reject or fail to reject the Null Hypothesis? Is the manager right?

Explanation / Answer

1) the null hypothesis = HO= U= 24

THE ALTERNATE HYPOTHESIS = Ha= u >24

2) as the distribution is normal the z test can be used

3) as we are using the z test

alpha = 0.05 and the test is right tailed test therefore

the critical regio = z>1.96

4) test static = (25.1 - 24)/ (7.9/sqrt(25))

= 0.69

5) as the z = 0.69<1.96

there fore we will accept the null hypothesis

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