Consider the following to answer the question(s) below:
Suppose that a report indicates that 28% of Canadians have experienced difficulty in making mortgage payments. Further suppose that a news organization randomly sampled 400 Canadians from 10 cities 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 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

To determine if the problem is more severe among the sampled cities, we need to conduct a hypothesis test. 
The null hypothesis is that the proportion of Canadians who have difficulty making mortgage payments in these 10 cities is the same as the national average (28%). 
The alternative hypothesis is that the proportion in these cities is greater than 28%. 
We can use a one-sample proportion test with a significance level of 0.05. 
Calculating the test statistic, we get: 
z = (0.34 - 0.28) / sqrt((0.28)(0.72)/400) = 2.67 
Since the calculated z-score is greater than the critical value of 1.645 (for a one-tailed test with alpha=0.05), we reject the null hypothesis and conclude that the problem of difficulty in making mortgage payments is more severe among these 10 cities.

Consider the Following to Answer the Question(s) Below