Question

The following contingency table represents the relationship between the age of a young adult and the type of movie preference

                               18-23 yr 24-29 yr 30-35 yr                                                                           

Science Fiction 14 9 8

Comedy 7 10 12

At the 0.05 level of significance, test the claim that the adult age and movie preference are independent (no relationship).

1. H0:

             H1:

2. Test Statistic:

3. Critical Region/Critical Value:

4. Decision about H0:

Answer 1

The test claim that the adult age and movie preference are independent (no relationship).

So , Hypothesis is ,

H0 : Adult age and movie preference are independent (no relationship).

H1 : Adult age and movie preference are dependent (relationship).

We have to perform Chi-square independence test.

Test statistic :

Chi-square test statistic:

Where,
O is observed frequency

E is expected frequency

Expected frequency -

Where ,

Ri corresponds to the total sum of elements in i^th row

Cj corresponds to the total sum of elements in j^th column

Calculation :

The row and column total have been calculated and they are shown below:

The table below shows the calculations to obtain the table with expected values:

Based on the observed and expected values, the squared distances can be computed according to the following formula: (E - O)^2/E

So, test statistics is ,

= 3.124

Critical Value :

Given , significance level = = 0.05

Degrees of freedom = ( R - 1 )( C - 1 ) = ( 2 - 1 )( 3 - 1 ) = 2

So Chi-square critical value for = 0.05 with df = 2 is,

= 5.991

Critical Region = { : > 5.991}

Decision about null hypothesis H0 :

It is observed that test statistic ( = 3.124 ) is less than = 5.991

So, fail to reject null hypothesis.

Conclusion :

There is sufficient evidence to conclude that Adult age and movie preference are independent (no relationship )