Question

A recent national survey found that high school students watched an average (mean) of 7.6 movies per month with a population standard deviation of 0.9. The distribution of number of movies watched per month follows the normal distribution. A random sample of 39 college students revealed that the mean number of movies watched last month was 7.1. At the 0.05 significance level, can we conclude that college students watch fewer movies a month than high school students?

Answer 1

Answer:

We conclude that college students watch fewer movies a month than high school students at the 0.05 significance level.

Step-by-step explanation:

We are given that a recent national survey found that high school students watched an average (mean) of 7.6 movies per month with a population standard deviation of 0.9.

A random sample of 39 college students revealed that the mean number of movies watched last month was 7.1.

Let $\mu$ = mean number of movies watched by college students last month.

So, Null Hypothesis, $H_0$ : $\mu \geq$ 7.6 movies      {means that college students watch higher or equal movies a month than high school students}

Alternate Hypothesis, $H_A$ : $\mu$ < 7.6 movies     {means that college students watch fewer movies a month than high school students}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

                          T.S. =  $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$  ~ N(0,1)

where, $\bar X$ = sample mean number of movies watched last month = 7.1

            σ = population standard deviation = 0.9

            n = sample of college students = 39

So, the test statistics  =  $\frac{7.1-7.6}{\frac{0.9}{\sqrt{39} } }$

                                       =  -3.47

The value of z test statistics is -3.47.

Now, at 0.05 significance level the z table gives critical value of -1.645 for left-tailed test.

Since our test statistic is less than the critical value of z as -3.47 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that college students watch fewer movies a month than high school students.