Question

Revenue for a full-service funeral. According to the National Funeral Directors Association (NFDA), the nation's 19,000 funeral homes collected an average of \(7,180 per full-service funeral in 2014 (www.nfda.org). A random sample of 36 funeral homes reported revenue data for the current year. Among other measures, each reported its average fee for a full-service funeral. These data (in thousands of dollars) are shown in the following table.

a. What are the appropriate null and alternative hypotheses to test whether the average full-service fee of U. S. funeral homes this year is less than \)7,180?

b. Conduct the test at\(\alpha = 0.05\). Do the sample data provide sufficient evidence to conclude that the average fee this year is lower than in 2014?

c. In conducting the test, was it necessary to assume that the population of average full-service fees was normally distributed? Justify your answer

Short answer

The null and the alternative hypotheses are\({H_0}:\mu = \$ 7,180\)and\({H_a}:\mu < \$ 7,180\)

Step-by-step solution

Given information

In 2014, the nation's 19,000 funeral homes collected an average of $7,180 per full-service funeral, according to the NFDA.

Concept of the null and the alternative hypothesis

The null hypothesis of a test always predicts no effect or no association between variables, while the alternative hypothesis states your research's prediction of an effect or relationship.

Setting up the null and the alternative hypothesis

a.

Let\(\mu \)be the average full-service fee of the U.S funeral homes in the present year.

Null hypothesis:

\({H_0}:\mu = \$ 7,180\)

The average full-service fee of U.S. funeral homes in the present year is $7,180.

Alternative hypothesis:

\({H_a}:\mu < \$ 7,180\)

That is, the average full-service fee of U.S. funeral homes in the present year is less than $7,180.