Question

# Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between...

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 12 13 34 Science Fiction 14 11 5 30 Comedy 9 8 12 29 Column Total 32 31 30 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 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.

H0: Age and movie preference are not 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?

binomial

uniform    Student's t

chi-square

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.

The statistical software output for this problem is:

Hence,

a) Level of significance = 0.05

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

Option C is correct.

b) Test statistic = 5.841

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.

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