Question

Movie Theater Attendance The data shown are the weekly admissions, in millions, of people attending movie theaters over three different time periods. At α = 0.05, is there a difference in the means for the weekly attendance for these time periods?

Use the traditional method of hypothesis testing unless otherwise specified.

a. State the hypotheses and identify the claim.

b. Find the critical value.

c. Compute the test value.

d. Make the decision.

e. Summarize the results.

1950–1974	1975–1990	1991–2000
58.0	17.1	23.3
39.9	19.9	26.6
25.1	19.6	27.7
19.8	20.3	26.5
17.7	22.9	25.8

H₀: μ₁ = μ₂ = μ₃. H₁: At least one mean is different from the others (claim); C.V. = 3.89; d.f.N. = 2; d.f.D. = 12; α = 0.05; F = 1.89; do not reject. There is not enough evidence to support the claim that at least one mean is different from the others.

Answer 1

1) Null and Alternative Hypothesis:

H₀: μ₁ = μ₂ = μ₃.

H₁: At least one mean is different from the others

2) Critical value of F = 3.885 at 5% los and (2,12) df from F- tables

Reject H0 if test statistic F > F critical value (=3.885)

3) From the given data

						Total	Ti^2/ni
1950-1974	58	39.9	25.1	19.8	17.7	160.5	5152.05
1975-1990	17.1	19.9	19.6	20.3	22.9	99.8	1992.008
1991-2000	23.3	26.6	27.7	26.5	25.8	129.9	3374.802
					Total G	390.2	10518.86

ANOVA Table:

Here F-value = 1.89 < F critical value so we accept H0

Thus we conclude that there is no  difference in the means for the weekly attendance for these time periods.

i.e. There is not enough evidence to support the claim that at least one mean is different from the others.