Question

We have constructed a 95% confidence interval for the population mean income
for the neighborhood. The confidence interval is ($15,040, $15,300). In order to
be eligible for government aid, a neighborhood must have an average income of
$15,000 or less. Based upon the confidence interval we can conclude that the
neighborhood is:
a. Definitely not eligible for aid.
b. Probably not eligible for aid.
c. Probably eligible for aid.
d. Definitely eligible for aid.
e. None of the above answers is correct.

Answer 1

Answer:

We have constructed a 95% confidence interval for the population mean income
for the neighborhood. The confidence interval is ($15,040, $15,300). In order to
be eligible for government aid, a neighborhood must have an average income of
$15,000 or less. Based upon the confidence interval we can conclude that the
neighborhood is:
a. Definitely not eligible for aid.
b. Probably not eligible for aid.
answer: c. Probably eligible for aid.
d. Definitely eligible for aid.
e. None of the above answers is correct.

$15000 is less than the lower limit of the 95% CI. We are 95% confident that population mean income falls in the interval ($15,040, $15,300). $15000 is less than the population mean income.