Question

Suppose that 28% of all Americans have experienced times when they haven’t been able to afford sufficient food. Separately, you sample 801 Americans who are financially less well-off than average Americans and find that 38% reported that there had been times in the last year when they had not been able to afford sufficient food. Does this indicate that the problem is more severe among those American who are less well-off? Test an appropriate hypothesis and state your conclusion. Make sure to check any necessary conditions and to state a conclusion in the context of the problem. Was your test one-tail upper tail, one-tail lower tail, or two-tail? Explain why you chose that kind of test in this situation. Find and explain what your P-value means in this context.

Answer 1

We will conduct Z-test for one population proportion as we need to test whether the proportion of Americans who are  financially less well-off than average Americans are significantly greater than 28%

Here, we use one-tail upper tail test because we want to check the condition whether proportion of Americans who are  financially less well-off than average Americans are significantly greater than 28% . So, our alternate hypothesis is p > 0.28 which is one direction only.

We perform Z-test for one population proportion as:

Since, Z = 6.303 > Z_c ( 1.64 ) , we reject null hypothesis.

Conclusion :

Hence, There is enough evidence to conclude that the problem of "not been able to afford sufficient food " is more severe among those American who are less well-off.