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 8 15 11 34 Science Fiction 15 12 3 30 Comedy 10 10 9 29 Column Total 33 37 23 93 (a) What is the level of significance? 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 not 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? binomial chi-square 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)

level of significance =0.05

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

b)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	18-23	24-29	30-35	Total
	Drama	12.065	13.527	8.409	34
	Science fiction	10.645	11.935	7.419	30
	Comedy	10.290	11.538	7.172	29
	total	33	37	23	93
chi square    χ2	=(Oi-Ei)2/Ei	18-23	24-29	30-35	Total
	Drama	1.369	0.160	0.799	2.3284
	Science fiction	1.782	0.000	2.632	4.4143
	Comedy	0.008	0.205	0.466	0.6790
	total	3.1590	0.3657	3.8969	7.422
test statistic X2 =		7.422

Are all the expected frequencies greater than 5? :Yes

What sampling distribution will you use? chi-square

degrees of freedom =(row-1)*(column-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.