Question

In: Statistics and Probability

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 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.

Solutions

Expert Solution

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.


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