Answered

Students in 7th and 8th grade were asked the types of movies they prefer. The results of the survey are shown in the table below:

\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & 7th Grade & 8th Grade & Total \\
\hline
Drama & 11\% & 15\% & 26\% \\
\hline
Action & 25\% & 19\% & 44\% \\
\hline
Comedy & 14\% & 16\% & 30\% \\
\hline
Total & 50\% & 50\% & 100\% \\
\hline
\end{tabular}

Which statements are correct? Check all that apply.

A. More 7th graders were surveyed than 8th graders.

B. The marginal relative frequency for action movies is 44%.

C. The joint relative frequency for 8th graders who like comedy movies is 16%.

D. Most students prefer drama movies.

E. Half of the 7th graders prefer action movies.



Answer :

GinnyAnswer
Let's analyze the given statements one by one, using the provided survey data from the table:

1. More 7th graders were surveyed than 8th graders
- From the table, the percentage of 7th graders surveyed is [tex]\(50\%\)[/tex] and the percentage of 8th graders surveyed is also [tex]\(50\%\)[/tex].
- Since both 7th and 8th graders were surveyed evenly at [tex]\(50\%\)[/tex] each, this statement is not correct.

2. The marginal relative frequency for action movies is [tex]\(44\%\)[/tex]
- The table shows that the total percentage of students who prefer action movies is [tex]\(44\%\)[/tex].
- This directly matches the given data, so this statement is correct.

3. The joint relative frequency for 8th graders who like comedy movies is [tex]\(16\%\)[/tex]
- According to the table, [tex]\(16\%\)[/tex] of 8th graders prefer comedy movies.
- This directly matches the given data, so this statement is correct.

4. Most students prefer drama movies
- From the table, the total percentage for each movie type is:
- Drama: [tex]\(26\%\)[/tex]
- Action: [tex]\(44\%\)[/tex]
- Comedy: [tex]\(30\%\)[/tex]
- Action movies have the highest total percentage at [tex]\(44\%\)[/tex], not drama movies.
- Therefore, this statement is not correct.

5. Half of the 7th graders prefer action movies
- The table shows that [tex]\(25\%\)[/tex] of 7th graders prefer action movies.
- [tex]\(25\%\)[/tex] is indeed half of the [tex]\(50\%\)[/tex] of the total 7th graders surveyed.
- Therefore, this statement is correct.

Based on the analysis:

- Statement 1: Incorrect
- Statement 2: Correct
- Statement 3: Correct
- Statement 4: Incorrect
- Statement 5: Correct

So the statements that are correct are:

- The marginal relative frequency for action movies is [tex]\(44\%\)[/tex].
- The joint relative frequency for 8th graders who like comedy movies is [tex]\(16\%\)[/tex].
- Half of the 7th graders prefer action movies.