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State the null and alternative hypotheses.

A sociologist was interested in determining if there was 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. Use a Chi-Square independence test to determine if age and type of movie preferred are independent at the [tex]$5\%$[/tex] level of significance.

\begin{tabular}{|c|c|c|c|c|}
\hline & \begin{tabular}{c}
[tex]$18-23$[/tex] years \\
old
\end{tabular} & \begin{tabular}{c}
[tex]$24-29$[/tex] years \\
old
\end{tabular} & \begin{tabular}{c}
[tex]$30-35$[/tex] years \\
old
\end{tabular} & Totals \\
\hline Drama & 8 & 15 & 11 & 34 \\
\hline \begin{tabular}{c}
Science \\
Fiction
\end{tabular} & 12 & 10 & 8 & 30 \\
\hline Comedy & 9 & 8 & 12 & 29 \\
\hline Totals & 29 & 33 & 31 & 93 \\
\hline
\end{tabular}

State the Null Hypothesis.

Sagot :

GinnyAnsweridn
Certainly! Let's outline the null and alternative hypotheses for the Chi-Square test of independence:

### Null Hypothesis ( [tex]\( H_0 \)[/tex] )
The null hypothesis states that there is no relationship between the age of a young adult and the type of movie preferred. In other words, age and movie preference are independent.

### Alternative Hypothesis ( [tex]\( H_1 \)[/tex] )
The alternative hypothesis states that there is a relationship between the age of a young adult and the type of movie preferred. In other words, age and movie preference are not independent.

Mathematically, these can be expressed as:
- Null Hypothesis ([tex]\( H_0 \)[/tex]): Age of a young adult and type of movie preferred are independent.
- Alternative Hypothesis ([tex]\( H_1 \)[/tex]): Age of a young adult and type of movie preferred are not independent.
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