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LiRa [457]
3 years ago
10

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 o

ld) 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

Mathematics
1 answer:
Alik [6]3 years ago
5 0

Answer:

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

Step-by-step 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:

<em>H₀</em>: Age of a young adult and movie preference are independent.

<em>Hₐ</em>: 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}{\frac{(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}\times \text{Column Total}}{\text{Total}}

The Chi-square test statistic value is:

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

The significance level of the test is, <em>α</em> = 0.05.

The degrees of freedom of the test is,

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

   = (3 - 1)(3 - 1)

   = 2 × 2

   = 4

Compute the <em>p</em>-value as follows:

<em>p</em>-value = 0.6266

*Use a Chi square table.

As the <em>p-</em>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.

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