Statistics

1.  What are the normality assumptions needed for a sampling distribution of Xbar and a proportion?

2. An actuary wants to prove that the unofficial drinking age is not necessarily 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 16.  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.

a. Describe the null and alternative hypotheses

b.Choose a significance level that makes sense to you and conduct the test statistic.

c.Interpret your results.

3. A research analyst disputes the trade group’s prediction that back to school spending will average $500 per family this year. She believes that average spending will differ significantly. She decides to conduct a test on a sample of 40 households with a sample mean of $522.  She believes that spending is normally distributed with a population sd of $50. She wants to conduct this test at a 5% significance level. Explain the hypotheses and conduct the test for the claim and then interpret your results.

4. What are the three approaches to conducting hypothesis tests. Describe how to use them.