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: $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the sample proportion, $p_0$ is the population proportion, and $n$ is the sample size. Here, $\hat{p} = \frac{136}{400} = 0.34$, $p_0 = 0.28$, and $n = 400$. Plugging these values into the formula gives a z-value of approximately 2.67, indicating the problem is more severe in these cities compared to the national average.

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