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	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 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 not independent.

H₀: Age and movie preference are 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?

chi-square

binomial    

uniform

Student's t

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

(a) The level of significance here is 5%, i.e.

The null and alternative hypotheses are: H0: Age and movie preference are independent.
H1: Age and movie preference are not independent.

(b) First, we need to compute the expected frequency for each cell by obtaining the product of itds corresponding row and column total.

For eg, for 18-23 age group that prefers drama, the expected frequency would be

Similarly, for the rest,

All the expected frequencies are greater than 5.

The value of the chi-square statistic for the sample can be calculated using the formula:

The sampling distribution used is chi square.

(c) In order to estimate the p value, we must compare the chi square test statistic with the tabled / critical value for (No. of rows-1)(No. of columns-1) = (3-1)(3-1) = 4 df

Find the value that is greater than 2.239 in the row corresponding to 4 df:

We find that the p value lies between 0.5 and 0.75.Hence, the correct option is 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.