Question

A marketing organization for apartment building owners advertises that one-bedroom

apartments within one-half mile of the campus rent on average for $725 per month. A

reporter for the student newspaper is writing an article on the cost of off-campus housing.

Her sample of 16 one-bedroom apartments in the one-half mile radius results in a sample

average of $750 with a sample standard deviation of $55. Does this data lead the reporter to

conclude at a 10% significance level that average rent is actually greater than the amount

claimed by the marketing organization?

Answer 1

Solution:

Given: A marketing organization for apartment building owners advertises that one-bedroom apartments within one-half mile of the campus rent on average for $725 per month.

Mean =

Sample size = n = 16

Sample mean =

Sample standard deviation = s = 55

significance level = 10% = 0.10

We have to test if  this data lead the reporter to conclude at a 10% significance level that average rent is actually greater than the amount claimed by the marketing organization.

that is: test if

Step 1) State H0 and H1:

Vs

( Right tailed test)

Step 2) Test statistic:

Step 3) Critical value:

df = n - 1 = 16 - 1 = 15

One tail area =  significance level = 10% = 0.10

t critical value = 1.341

Step 4) Decision Rule:

Reject null hypothesis H0, if t test statistic value > t critical value = 1.341, otherwise we fail to reject H0

Since t test statistic value = t = 1.818 > t critical value = 1.341, we reject null hypothesis H0.

Step 5) Conclusion:

This data lead the reporter to conclude at a 10% significance level that average rent is actually greater than the amount claimed by the marketing organization.