A report on the U.S.economy indicates that 28% of Americans have experienced difficulty in making mortgage payments.A news organization randomly sampled 400 Americans from 10 cities named the "fastest dying cities in the U.S." (Forbes Magazine, August 2008) and found that 136 reported such difficulty.Does this indicate that the problem is more severe among these cities? The correct value of the test statistic for testing this claim is ________________________ .
A)z = -1.28.
B)z = -2.67
C)z = 2.67
D)z = 1.96
E)z = -1.28

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula for a proportion z-test. Given that 136 out of 400 sampled individuals experienced difficulty, the sample proportion is 136/400 = 0.34. The null hypothesis proportion (population proportion) is 0.28. The test statistic formula is $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the sample proportion, $p_0$ is the null hypothesis proportion, and $n$ is the sample size. Plugging in the values, we get $z = \frac{0.34 - 0.28}{\sqrt{\frac{0.28(1-0.28)}{400}}}$, which calculates to approximately 2.67, indicating that the sample proportion is significantly higher than the population proportion, suggesting the problem is more severe in these cities.

A Report on the U