Question

According to a recent survey of the 18​,000 funeral homes of a certain​ nation, funeral homes collected an average of​6,700 per​ full-service funeral last year. 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 accompanying table. Complete parts a through c below.\

7.4	9.4	5.2	8.5	7.7	6.3
6.2	8.3	6.4	11.6	6.3	5.8
7.2	6.1	5.2	6.5	6.1	7.5
7.2	6.4	6.3	5.2	6.9	5.6
9.3	7.5	7.4	5.8	7.1	5.9
6.9	7.5	5.9	5.4	7.7	6.9

a. What are the appropriate null and alternative hypotheses to test whether the average​ full-service fee of funeral homes this year exceeds ​$ 6,700​?

A. H0​: μ=6.7

Ha​: μ > 6.7

B. H0​: μ ≠ 6.7

Ha​:μ = 6.7

C. H0​: μ = 6.7

Ha​: μ < 6.7

D. H0​: μ = 6.7

Ha​:μ ≠ 6.7

b. Conduct the test at α = 0.10. Do the sample data provide sufficient evidence to conclude that the average fee this year is higher than last​ year?

Find the test statistic.

z = ___________ ​(Round to two decimal places as​ needed.)

Find the​ p-value.

​p- value = _________ ​(Round to three decimal places as​ needed.)

State the result of this test.

A. H0 is rejected. There is insufficient evidence at the α=0.10 level of significance to conclude that the average fee this year is higher than last year.

B. H0 is not rejected. There is sufficient evidence at the α=0.10 level of significance to conclude that the average fee this year is higher than last year.

C. H0 is not rejected. There is insufficient evidence at the α=0.10 level of significance to conclude that the a fee this year is higher than last year.

D. H0 is rejected. There is sufficient evidence at the α=0.10 level of significance to conclude that the average fee this year is higher than last year.

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

A. ​Yes, because the sample size is greater than 30.

B. ​No, because the sample size is greater than 30.

C. ​Yes, because the sample size is less than 40.

D. ​No, because the sample size is less than 40.

Answer 1

Solution:-

a) (A) State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u < 6.70
Alternative hypothesis: u > 6.70

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.10. The test method is a one-sample z-test.

Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).

SE = s / sqrt(n)

S.E = 0.2581

z = (x - u) / SE

z = 0.943

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a z statistic test statistic of 0.943.

Thus the P-value in this analysis is 0.173.

Interpret results. Since the P-value (0.173) is greater than the significance level (0.10), we cannot reject the null hypothesis.

(C) H0 is not rejected. There is insufficient evidence at the α=0.10 level of significance to conclude that the a fee this year is higher than last year.

c) (A) Yes, because the sample size is greater than 30.