The average moviegoer sees 8.5 movies a year. A moviegoer is defined as a person

Question

The average moviegoer sees 8.5 movies a year. A moviegoer is defined as a person who sees at least one movie in a theater in a 12 month period. A random sample of 41 moviegoers from a large university revealed that the average number of movies seen per person was 8.7. The population standard deviation is 3.2 movies. At the 0.01 level of significance, can it be concluded that this represents a difference from the national average?

a) Find the critical value (s). Enter the values in ascending order. Round the answer to two decimal places.

b) Compute the test value. Always round t score values to three decimal places

c) Do or do not reject the hypothesis

d) **if not rejected there is not enough evidence to support the claim

Explanation / Answer

Part-a

Null hypothesis H0: =8.5 and alternative hypothesis ha: 8.5

As population standard deviation is known and sample size n>30, so we will apply z-test of one mean.

So, at 0.01 level of significance critical values are -2.58 and 2.58

Part-b

Test statistic value Z= (Mean-8.5)/(/sqrt(n))

=(8.7-8.5)/(3.2/sqrt(41))

=0.40

Part-c

As Calculated Z<2.58, we do not reject the null hypothesis

Part-d

There is not enough evidence to support the claim this represents a difference from the national average.

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