The Results of a Recent National Survey Reported That 70

Essay

The results of a recent national survey reported that 70% of Americans recycle at least some of the time. As partof their final project in statistics class, Nayla and Roberto survey 5 random students on campus and ask them ifthey recycle at least some of the time. They then repeat this experiment 1000 times. The results of their researchare shown below. $\begin{array}{l|c|c|c|c|c|c}X \text { (number who recycle out of 5) } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Frequency } & 2 & 27 & 139 & 305 & 358 & 169\end{array}$
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?