A Sociologist Believes That Families That Eat at Least One

Essay

A sociologist believes that families that eat at least one meal a day together (without theinterference of any other media) will have better communication skills. The sociologistconducts a study to see if there is a difference in the proportion of meals that are eatentogether as a family for families living in a rural setting compared to families living in anurban setting. She collects a random sample from each population and records theproportion of test subjects that reported that they had eaten at least 3 meals per weektogether as a family. The data is summarized in the table below. Assume the all conditionsfor proceeding with a two-sample test have been met. $$\begin{array} { | l | l | } \hline \text { Rural } & \text { Urban } \\ \hline n _ { 1 } = 75 & n _ { 2 } = 140 \\ \hline x _ { 1 } = 12 & x _ { 2 } = 40 \\ \hline \end{array}$$ Find the z test statistic (rounded to the nearest hundredth) and p-value (rounded to the nearest thousandth) for testing the hypothesis that the population proportions are different. At the 5% significance level, state the correct conclusion regarding the null hypothesis $\mathrm { H } _ { 0 } : \text { prural } = \mathrm { p } _ { u r b a n }$ . Round all calculations to the nearest hundredth.