A random sample of 10 colleges was taken. The mean rate of graduation within fou

Question

A random sample of 10 colleges was taken. The mean rate of graduation within four years was 43.5% with a margin of error of 7.0%. The distribution of graduation rates is Normal.

We are 95% confident that the population mean is between 36.5 % and 50.5 %.

Can we reject a population mean percentage of 23.2% on the basis of these numbers?

A.Yes, reject 23.2%. Since 23.2% is not in the interval, it is not plausible the population graduation rate is 23.2%.

B.Yes, reject 23.2%. Since 23.2% is in the interval, it is not plausible the population graduation rate is 23.2%.

C.No, do not reject 23.2%. Since 23.2% is not in the interval, it is plausible the population graduation rate is 23.2%.

D.No, do not reject 23.2%. Since 23.2% is in the interval, it is plausible the population graduation rate is 23.2%.

E.There is insufficient information to make a decision regarding the rejection of 23.2%.The sample size of 10 colleges is less than the required 25.

Explanation / Answer

Solution :

n = 10

sample mean = 43.5%

Margin of error = E = 7%

Lower limit = 36.5%

Upper limit = 50.5%

A.Yes, reject 23.2%. Since 23.2% is not in the interval, it is not plausible the population graduation rate is 23.2%.

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