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

question 21

Multiple Choice

A researcher believes that children who attend elementary school in a rural setting have lowerobesity rates then children who attend elementary school in an urban setting. The researchercollects a random sample from each population and records the proportion of children in eachsample who were clinically obese. The data is summarized in the table below. Assume the allconditions for proceeding with a two-sample test have been met.

$\begin{array}{|l|l|}\hline \text { Rural } & \text { Urban } \\\hline n_{1}=95 & n_{2}=100 \\\hline x_{1}=14 & x_{2}=26 \\\hline\end{array}$

Find the z-statistic (rounded to the nearest hundredth) and p-value (rounded to the nearestthousandth) for this hypothesis test. Using a 5% significance level, state the correct conclusionregarding the null hypothesisH0:prural=purban.

• A)z=-1.95, p=0.026. There is not sufficient evidence to reject the null hypothesis.
• B)z=-1.85, p=0.032. There is sufficient evidence to accept the null hypothesis.
• C)z=-1.95, p=0.026. There is sufficient evidence to reject the null hypothesis.
• D)z=1.95, p=0.026. There is sufficient evidence to prove that the population proportions are thesame.

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Definitions:

Long-term Trend

This is a sustained movement in data over a long period, indicating a general direction in which something is developing or changing.

Time Series

Sequenced data points collected or recorded at time intervals, often analyzed to identify trends, cyclical patterns, or to forecast.

Random Variation

Fluctuations in data or experimental results due to unpredictable changes in variables or conditions.

Time Series

A sequence of data points collected or recorded at successive points in time, often analyzed to identify trends, cycles, and seasonal variations.