A survey found that in a random sample of 72 families, 21 owned dogs. A survey done 15 years ago found that in a random sample of 63 families, 28 owned dogs. At $\alpha = 0.05$, has the proportion of dog owners changed over the 15 -year period? USe the $P$-value method.
A) There is not enough information to draw a conclusion.
B) No. There is not sufficient evidence to conclude that the proportion of dog owners has changed.
C) Yes. There is sufficient evidence to conclude that the proportion of dog owners has changed.

Question

Quizplus · Accepted Answer

To determine if the proportion of dog owners has changed, we can use a two-proportion z-test. The null hypothesis (H0) is that the proportions are equal (no change), and the alternative hypothesis (Ha) is that the proportions are not equal (there is a change). Calculating the test statistic and corresponding p-value allows us to compare it with the significance level ($\alpha = 0.05$). Without the exact p-value calculation here, the correct interpretation is that if the evidence does not strongly contradict the null hypothesis (meaning the p-value is greater than 0.05), we do not reject H0. Thus, the statement that there is not sufficient evidence to conclude that the proportion of dog owners has changed is the correct interpretation, assuming the p-value did not indicate a significant difference.

A Survey Found That in a Random Sample of 72 α=0.05\alpha = 0.05α=0.05

A Survey Found That in a Random Sample of 72 $\alpha = 0.05$