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Use the data table to answer the following questions.

A teacher is doing a sample survey on the average number of hours students at CHS spend watching television per week. There are 1000 students in the school. She picks a sample of 50 students by selecting 10 students who have [tex]$1^{\text{st}}$[/tex] period English, 10 students who have [tex]$1^{\text{st}}$[/tex] period Math, 10 students who have [tex]$1^{\text{st}}$[/tex] period History, 10 students who have [tex]$1^{\text{st}}$[/tex] period Science, and 10 students who have [tex]$1^{\text{st}}$[/tex] period PE.

\begin{tabular}{|c|c|}
\hline
\begin{tabular}{c}
Number of Hours per \\
Week
\end{tabular} & \begin{tabular}{c}
Number of \\
Students
\end{tabular} \\
\hline
[tex]$0-1$[/tex] & 4 \\
\hline
[tex]$2-4$[/tex] & 8 \\
\hline
[tex]$5-7$[/tex] & 20 \\
\hline
[tex]$8-10$[/tex] & 10 \\
\hline
[tex]$10+$[/tex] & 8 \\
\hline
\end{tabular}

1. Is this sample representative or biased?

2. What proportion of students watch [tex]$5-7$[/tex] hours of television per week?

3. Predict the total number of students who watch [tex]$5-7$[/tex] hours of television per week.



Answer :

GinnyAnswer
Certainly! Let's break down and solve these questions step-by-step.

### 1. Is this sample representative or biased?
The teacher picked a sample of 50 students by choosing 10 students from each of the first-period classes: English, Math, History, Science, and PE. This method of selecting the sample is biased. It does not represent the entire student body fairly because it only includes students based on their first-period class. A more representative sample would involve randomly selecting students from the entire student body without considering their first-period class, ensuring that every student has an equal chance of being included.

### 2. What proportion of students watch [tex]$5-7$[/tex] hours of television per week?
We need to determine the proportion of students within the sample who watch between 5-7 hours of television per week.

- Total number of students in the sample: 50
- Number of students who watch 5-7 hours of television per week: 20

Proportion = (Number of students watching 5-7 hours per week) / (Total number of students in the sample)
Proportion = 20 / 50
Proportion = 0.4

Therefore, the proportion of students who watch 5-7 hours of television per week in the sample is 0.4 (or 40%).

### 3. Predict the total number of students who watch [tex]$5-7$[/tex] hours of television per week.
With the given proportion, we can predict how many students out of the total student body (1000 students) watch 5-7 hours of television per week.

Proportion of students (from the sample) watching 5-7 hours per week = 0.4
Total number of students at the school = 1000

Predicted number of students = Proportion Total number of students
Predicted number of students = 0.4 1000
Predicted number of students = 400

Thus, we can predict that approximately 400 students at the school watch 5-7 hours of television per week.

So, to summarize:
1. The sample is biased.
2. The proportion of students who watch 5-7 hours of television per week is 0.4.
3. The predicted total number of students who watch 5-7 hours of television per week is 400.

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