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?

Question

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?

Quizplus · Accepted Answer

The Answer is Since

\chi ^ { 2 } = 0.975 < \chi _ { 0.05 } ^ { 2 } = 11.070

(with 5 degrees of freedom), we do not reject the null hypothesis. There is evidence at the

\alpha = 0.05

level that

\mathrm { X }

is a binomial random variable with

70 \%

and

\mathrm { p } = 0.7

.

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