The Results of a Recent National Survey Reported That $70 \%$

question 8

Short Answer

The results of a recent national survey reported that $70 \%$ of Americans recycle at least some of the time. As part of their final project in statistics class, Nayla and Roberto survey 5 random students on campus and ask them if they recycle at least some of the time. They then repeat this experiment 1000 times. The results of their research are shown below.
$\begin{array}{l|l|c|c|c|c|c}\mathrm{X} \text { (number who recycle out of 5) } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Frequency } & 2 & 25 & 139 & 306 & 356 & 172\end{array}$

Is there evidence to support the belief that the random variable $X$ , the number of students out of 5 who recycle at least some of the time, is a binomial random variable with $\mathrm { p } = 0.7$ at the $\alpha = 0.05$ level?

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Definitions:

Group Members

Individuals who belong to a specific collective or team working together towards common goals.

Committed Goals

Objectives that an individual is personally invested in achieving, often involving dedication and a significant amount of effort.

Science Fiction

A genre of literature and media that explores imaginative and futuristic concepts based on science.

Test Validity

The degree to which a test accurately measures what it is intended to measure, ensuring that the test results are relevant and meaningful for its purpose.