Question

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

	Person's Age
Movie	18-23 yr	24-29 yr	30-35 yr	Row Total
Drama	7	12	15	34
Science Fiction	14	9	7	30
Comedy	8	7	14	29
Column Total	29	28	36	93

(a) What is the level of significance?
0.05

State the null and alternate hypotheses.

H₀: Age and movie preference are independent. & H₁: Age and movie preference are independent.

H₀: Age and movie preference are not independent. & H₁: Age and movie preference are not independent.     

H₀: Age and movie preference are independent. & H₁: Age and movie preference are not independent.

H₀: Age and movie preference are not independent. & H₁: Age and movie preference are independent.

(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?

Student's t

chi-square     

binomial

uniform

normal

What are the degrees of freedom?
_____

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

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 or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.     

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.

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

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

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

Answer 1

The statistical software output for this problem is :

(a)

The level of significance = 0.05

H₀: Age and movie preference are independent.

& H₁: Age and movie preference are not independent.

(b)

Test statistics = 7.073

Yes

Chi square

degrees of freedom = 4

(c)

P-value > 0.100

(d)

Since the P-value > α, we fail to reject the null hypothesis.

(e)

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