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Mr. Acosta, a sociologist, is doing a study to see if there is arelationship between the age of a young adult (18 to 35 years old)and the type of movie preferred. A random sample of 93 adultsrevealed the following data. Test whether age and type of moviepreferred are independent at the 0.05 level.

	Person'sAge
Movie	18-23yr	24-29yr	30-35yr	RowTotal
Drama	8	17	9	34
Science Fiction	14	11	5	30
Comedy	8	10	11	29
ColumnTotal	30	38	25	93

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: Age and movie preference are notindependent.
H₁: Age and movie preference areindependent.H₀: Age and movie preference areindependent.
H₁: Age and movie preference are notindependent.    H₀: Age andmovie preference are not independent.
H₁: Age and movie preference are notindependent.H₀: Age and movie preference areindependent.
H₁: Age and movie preference areindependent.

(b) Find the value of the chi-square statistic for the sample.(Round the expected frequencies to at least three decimal places.Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

YesNo    

What sampling distribution will you use?

binomialnormal    uniformchi-squareStudent'st

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample teststatistic.

P-value > 0.1000.050 < P-value <0.100    0.025 < P-value <0.0500.010 < P-value < 0.0250.005 <P-value < 0.010P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis of independence?

Since the P-value > α, we fail to rejectthe null hypothesis.Since the P-value > α, wereject the null hypothesis.    Since theP-value ≤ α, we reject the null hypothesis.Sincethe P-value ≤ α, we fail to reject the nullhypothesis.

(e) Interpret your conclusion in the context of theapplication.

At the 5% level of significance, there is sufficient evidence toconclude that age of young adult and movie preference are notindependent.At the 5% level of significance, there is insufficientevidence to conclude that age of young adult and movie preferenceare not independent.