Question

The success of a major movie is often determined by the amount of money that a movie makes (in millions of dollars). Suppose we want to test the claim that movies with three different ratings (PG, PG-13, and R ratings) bring in the same amount of money on average, using a 0.05 significance level. Below are the ANOVA results of this analysis.

	df	SS	MS	F-value	Pr(>F)
Groups	2	44461.204	22230.602	2.781	.0774
Residuals	31	247806.1	7993.744
Total	33	292267.3

A. State the null and alternative hypotheses in symbols and in words

B. State the conclusion of the hypothesis test in context of the original claim.

Answer 1

Part A

Null hypothesis: H₀: Movies with three different ratings (PG, PG-13, and R ratings) bring in the same amount of money on average.

Alternative hypothesis: H_a: At least one group of movies with three different ratings (PG, PG-13, and R ratings) bring in different amount of money on average.

H₀: µ₁ = µ₂ = µ₃ versus H_a: At least one µ is different.

Or

H₀: µ₁ = µ₂ = µ₃ versus H_a: µ₁ ≠ µ₂ ≠ µ₃

H₀: µ₁ = µ₂ = µ₃ versus H_a: µ₁ = µ₂ ≠ µ₃

H₀: µ₁ = µ₂ = µ₃ versus H_a: µ₁ ≠ µ₂ = µ₃

B. State the conclusion of the hypothesis test in context of the original claim.

From given ANOVA table, we have

P-value = 0.0774

α = 0.05

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that Movies with three different ratings (PG, PG-13, and R ratings) bring in the same amount of money on average.