Question

According to a recent survey of the 23​,000 funeral homes of a certain​ nation, funeral homes collected an average o ​$ 6,500 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.

7.3	9.4	5.1	8.6	7.8	6.2
6.1	8.8	6.5	11.2	6.5	5.9
7.2	5.9	5.4	6.6	6.1	7.6
6.9	6.1	6.7	5.3	7.2	5.6
9.5	7.2	7.5	5.8	6.3	5.7
7.2	7.3	5.9	4.9	7.7	6.7

State the result of this test.

a. What are the appropriate null and alternative hypotheses to test whether the average​ full-service fee of funeral homes this year exceeds $ 6,500​?

A. H0​: μ=6.5

Ha​: μ>6.5

B. H0​: μ=6.5

Ha​: μ≠6.5

C. H0​: μ=6.5

Ha​: μ<6.5

D. H0​: μ≠6.5

Ha​: μ=6.5

b. Conduct the test at α=0.01.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 not rejectednot rejected. There is sufficients evidence at the α=0.01level of significance to conclude that the average fee this year is higher than last year.

B. H0 is not rejected. There is insufficient evidence at the α=0.01 level of significance to conclude that the average fee this year is higher than last year.

C. H0 is rejected. There is sufficient evidence at the α=0.01 level of significance to conclude that the average fee this year is higher than last year.

D. H0 is rejected. There is insufficient evidence at the α=0.01 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 less than 40.

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

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

Answer 1

The statistical software output for this problem is:

One sample Z hypothesis test:
μ : Mean of variable
H₀ : μ = 6.5
H_A : μ > 6.5

Hypothesis test results:

Variable	n	Sample Mean	Std. Err.	Z-Stat	P-value
Data	36	6.8805556	0.22469801	1.6936311	0.0452

Hence,

a) Hypotheses:

H0​: μ = 6.5

Ha​: μ > 6.5

Option A is correct.

b) z = 1.69

p - value = 0.045

Result: H0 is not rejected. There is insufficient evidence at the α=0.01 level of significance to conclude that the average fee this year is higher than last year. Option B is correct.

No, because the sample size is greater than 30. Option D is correct.