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 10 14 10 34 Science Fiction 11 9 10 30 Comedy 7 9 13 29 Column Total 28 32 33 93 (a) What is the level of significance

Answer 1

There is a relationship between the age of a young adult and the type of movie preferred.

Explanation:

In this case we need to test whether there is a significance relationship between the age of a young adult and the type of movie preferred.

The hypothesis can be defined as:

H₀: Age of a young adult and movie preference are independent.

Hₐ: Age of a young adult and movie preference are not independent.

The test statistic is given as follows:

`\chi^(2)=\sum\limits^(n)_(i=1){((O_(i)-E_(i))^(2))/(E_(i))}`

Consider the table below.

The formula to compute the expected frequencies is:

`E_(i)=\frac{\text{Row Total}* \text{Column Total}}{\text{Total}}`

The Chi-square test statistic value is:

`\chi^(2)=\sum\limits^(n)_(i=1){((O_(i)-E_(i))^(2))/(E_(i))}=2.6013`

The significance level of the test is, α = 0.05.

The degrees of freedom of the test is,

df = (r - 1)(c - 1)

= (3 - 1)(3 - 1)

= 2 × 2

= 4

Compute the p-value as follows:

p-value = 0.6266

*Use a Chi square table.

As the p-value is more than the significance level the null hypothesis was failed to be rejected.

Thus, concluding that there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred.