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 null and alternative hypotheses for testing this claim are A) $H _ { 0 } : p = 0.28$ and $H _ { A } : p 0.28$ C) $H _ { 0 } : p \neq 0.28$ and $H _ { A } : p = 0.28$ D) $H _ { 0 } : p 0.28$ and $H _ { A } : p = 0.28$ E) $H _ { 0 } : p = 0.28$ and $H _ { A } : p \neq 0.28$

Question

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 null and alternative hypotheses for testing this claim are
A) $H _ { 0 } : p = 0.28$ and $H _ { A } : p < 0.28$
B) $H _ { 0 } : p = 0.28$ and $H _ { A } : p > 0.28$
C) $H _ { 0 } : p \neq 0.28$ and $H _ { A } : p = 0.28$
D) $H _ { 0 } : p > 0.28$ and $H _ { A } : p = 0.28$
E) $H _ { 0 } : p = 0.28$ and $H _ { A } : p \neq 0.28$

Quizplus · Accepted Answer

The null hypothesis ($H_0$) typically represents the status quo or a statement of no effect, which in this case is that the proportion ($p$) of Americans having difficulty making mortgage payments in these cities is equal to the reported national average of 0.28. The alternative hypothesis ($H_A$) is what the study aims to test against the null hypothesis. Since the question is whether the problem is more severe in these cities, the alternative hypothesis should reflect an increase in the proportion, hence $p > 0.28$.

A Report on the U 28%28 \%28% Of Americans Have Experienced Difficulty in Making Mortgage Payments

A Report on the U $28 \%$ Of Americans Have Experienced Difficulty in Making Mortgage Payments