Question

moviegoers 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 47 moviegoers from a large university revealed that the average number of movies seen per person was 9.8. 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?
part 1 of 5
state the hypotheses and identify the claim with the correct hypothesis
$h_0: \mu = 8.5$ (claim dropdown)
$h_1: \mu \
eq 8.5$ (claim dropdown)
this hypothesis test is a (select dropdown) test.

Explanation:

Step1: Identify Hypotheses

The national average (population mean, $\mu$) is 8.5. The claim is if the university sample differs from this, so null hypothesis ($H_0$) is $\mu = 8.5$ (no difference), alternative ($H_1$) is $\mu
eq 8.5$ (difference, two - tailed).

Step2: Determine Test Type

Since $H_1$ has $
eq$, it's a two - tailed test. For $H_0$: $\mu = 8.5$ (not the claim, the claim is in $H_1$ as we are testing for a difference). Wait, correction: The claim is "a difference from the national average", so $H_1: \mu
eq 8.5$ is the claim, and $H_0: \mu = 8.5$ is the null. The test is two - tailed because we are checking for a difference (could be more or less).

Answer:

$H_0: \mu = 8.5$ (not the claim), $H_1: \mu
eq 8.5$ (claim). This hypothesis test is a two - tailed test.