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's Age
Movie	18-23 yr	24-29 yr	30-35 yr	Row Total
Drama	9	16	9	34
Science Fiction	9	10	11	30
Comedy	7	10	12	29
Column Total	25	36	32	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 are notindependent.

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 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?

Yes

No    

What sampling distribution will you use?

chi-square

binomial    

uniform

Student's t

normal

What are the degrees of freedom?


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

P-value > 0.100

0.050 < P-value <0.100    

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-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 > ?, we fail to rejectthe null hypothesis.

Since the P-value > ?, we reject the nullhypothesis.    

Since the P-value ? ?, we reject the nullhypothesis.

Since the P-value ? ?, we fail to reject thenull hypothesis.

(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 insufficient evidenceto conclude that age of young adult and movie preference are notindependent.