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.

Table

7.5 9.1 5.4 8.6 7.7 6.3

5.9 8.6 6.5 11.3 6.7 5.3

6.7 5.9 5.5 6.5 6.1 7.4

6.9 6.5 6.7 5.2 6.5 5.6

9.1 7.2 7.6 5.5 6.5 6.2

7.2 7.9 6.2 5.3 7.7 6.6

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​?

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 = ?

Find the p-value

p-value = ?

States the result of this test

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

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

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

D. H₀ is rejected. There’s 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. No because the sample size is less than 40

B. Yes, 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 greater than 30

Answer 1

H_0: mu 6.7 versus H_a: mu > 6.7 alpha = 0.10, x^Overbar = 6.23, s = 0.745, Squarerootn = Squareroot36 = 6, mu_0 = 6.7 Z = Squarerootn(x^OverBar - mu_0)/s = -3.7865 P-value = P(z greaterthanorequalto - 3.7865) = 0.9999 Result of the text option B Option B n greaterthanorequalto 30 (normality assumption).