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A recent national survey found that high school students watched an average (mean) of 7.8 movies per month with a population standard deviation of 0.5. The distribution of number of movies watched per month follows the normal distribution. A random sample of 30 college students revealed that the mean number of movies watched last month was 7.3. At the 0.05 significance level, can we conclude that college

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Answer:

Step-by-step explanation:

Given that :

Mean = 7.8

Standard deviation = 0.5

sample size = 30

Sample mean = 7.3 5.4772

The null and the alternative hypothesis is as follows;

[tex]\mathbf{ H_o: \mu \geq 7.8}[/tex]

[tex]\mathbf{ H_1: \mu < 7.8}[/tex]

The test statistics can be computed as :

[tex]z = \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \dfrac{7.3- 7.8}{\dfrac{0.5}{\sqrt{30}}}[/tex]

[tex]z = \dfrac{-0.5}{\dfrac{0.5}{5.4772}}[/tex]

[tex]z = - 5.4772[/tex]

The p-value at  0.05 significance level is:

p-value = 1- P( Z < -5.4772)

p value = 0.00001

Decision Rule:

The decision rule is to reject the null hypothesis if  p value is less than 0.05

Conclusion:

At  the 0.05 significance level,  there is sufficient information to reject the null hypothesis. Therefore ,we  conclude that college students watch fewer movies a month than high school students.