A Researcher Believes That Children Who Attend Elementary School in a Rural

Multiple Choice

A researcher believes that children who attend elementary school in a rural setting are more physically active then children who attend elementary school in an urban setting. The researcher collects a random sample from each population and records the proportion of children in each sample who reported participating in at least one hour of rigorous activity a day. The data is summarized in the table below. Assume the all conditions for proceeding with a two-sample test have been met.

$\begin{array}{|l|l|}\hline \text { Rural } & \text { Urban } \\\hline n_{1}=90 & n_{2}=78 \\\hline x_{1}=74 & x_{2}=55 \\\hline\end{array}$

Find the $z$ -statistic (rounded to the nearest hundredth) and p-value (rounded to the nearest thousandth) for this hypothesis test. Using a $5 \%$ significance level, state the correct conclusion regarding the null hypothesis, $\mathrm { H } _ { 0 }$ : prural = purban.

A) $z = 0.82 , p = 0.073$ . There is sufficient evidence to accept the null hypothesis.
B) $\mathrm { z } = - 1.79 , \mathrm { p } = 0.037$ . There is insufficient evidence to reject the null hypothesis.
C) $\mathrm { z } = 1.79 , \mathrm { p } = 0.037$ . There is sufficient evidence to reject the null hypothesis.
D) $z = 0.71 , p = 0.073$ . There is sufficient evidence to reject the null hypothesis.