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:
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:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}[/tex]
Consider the table below.
The formula to compute the expected frequencies is:
[tex]E_{i}=\frac{\text{Row Total}\times \text{Column Total}}{\text{Total}}[/tex]
The Chi-square test statistic value is:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}=2.6013[/tex]
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.
