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	6	13	15	34
Science Fiction	14	11	5	30
Comedy	9	8	12	29
Column Total	29	32	32	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 not 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

What sampling distribution will you use?

chi-square

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

Answer 1

(a) The level of significance = 0.05

** The null and alternate hypotheses:

H0: Age and movie preference are independent.

H1: Age and movie preference are not independent.

(b) The value of the chi-square statistic for the sample: 8.971

** Yes, all the expected frequencies are greater than 5.

** Sampling distribution: Chi-square.

** The degrees of freedom are 4.

(c) 0.050 < P-value < 0.100

>> Software Outputs:

Actual Values:
6 13 15
14 11 5
9 8 12

Expected Values:
10.6021 11.6989 11.6989
9.35484 10.3226 10.3226
9.04301 9.9785 9.9785

Chi-Squared Values:
1.99769 0.144697 0.931462
2.30656 0.0444556 2.74446
0.00020457 0.392288 0.409529

Chi-Square = 8.97134

Degrees of Freedom = 4

P-value = 0.0618198