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	9	13	12	34
Science Fiction	11	11	8	30
Comedy	8	7	14	29
Column Total	28	31	34	93

(a) What is the level of significance?
_____________-

State the null and alternate hypotheses.

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

No    

What sampling distribution will you use?

normal

binomial    

chi-square

uniform

Student's t

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

(a)

The level of significance is: 0.05

Hypotheses are:

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

(c)

Expected frequencies will be calculated as follows:

Following table shows the expected frequencies:

	Person's Age
Movie	18-23 yr	24-29 yr	30-35 yr	Row Total
Drama	10.237	11.333	12.43	34
Science Fiction	9.032	10	10.968	30
Comedy	8.731	9.667	10.602	29
Column Total	28	31	34	93

Following table shows the calculations for chi square test statistics:

O	E	(O-E)^2/E
9	10.237	0.149474358
11	9.032	0.428811337
8	8.731	0.061202726
13	11.333	0.2452033
11	10	0.1
7	9.667	0.735790731
12	12.43	0.014875302
8	10.968	0.80315682
14	10.602	1.08907791
Total		3.627592484

Following is the test statistics:

Are all the expected frequencies greater than 5?

Yes

What sampling distribution will you use?

chi-square

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (3-1)*(3-1)=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