Question

An actuary wants to prove that the unofficial drinking age is younger than 21. It is assumed the age is normally distributed with a known population standard deviation of 5. Let there be a sample of 25 millennials with an average drinking age of 17. The significance level should be strong because the actuary wants to use this test to show that 21 is not necessarily the most dangerous year to drive.

1. Describe the null and alternative hypotheses.
2. Choose a significance level that makes sense to you and conduct the test statistic.
3. Interpret your results.

Answer 1

Answer: We reject the null hypothesis.

Explanation:

Since we have given that

We claim that unofficial drinking age is younger than 21.

So, our hypothesis would be

Null hypothesis :
`\mu =21`

Alternate hypothesis :
`\mu>21`

Test statistic would be

`z=\frac{\bar{X}-\mu}{(\sigma)/(√(n))}\\\\z=(17-21)/((5)/(√(25)))\\\\z=(-4)/(1)\\\\z=-4`

According to question, p-value = 0

As p- value is less than 0.05 level of significance.

So, we reject the null hypothesis.