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

question 18

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.

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Definitions:

Emergent Norm Theory

A theory suggesting that norms in a group setting can develop spontaneously and influence the group's behavior.

Visually Surprising

Something that is unexpected or startling from a visual perspective, often eliciting a strong reaction or attention.

Unwanted Contact

Interactions or communications that are undesired or uninvited, potentially causing discomfort or distress to the recipient.

Collectives

Groups or aggregates of people or items that share common features or are considered together.