An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 1.5 years of the population mean. Assume the population of ages is normally distributed.

(a) Determine the minimum sample size required to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 1.8 years.

(b) The sample mean is 20 years of age. Using the minimum sample size with a 90% level ofconfidence, does it seem likely that the population mean could be within 10% of the samplemean? within 11% of the samplemean? Explain.

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(a) The minimum sample size required to construct a 90% confidence interval is

nothing

students.

(Round up to the nearest wholenumber.)

(b) The 90% confidence interval is (

nothing

,

nothing

). It

does

does not

seem likely that the population mean could be within 10% of the sample mean because 10% off from the sample mean would fall

outside

inside

the confidence interval. It

does not

does

seem likely that the population mean could be within 11% of the sample mean because 11% off from the sample mean would fall

outside

inside

the confidence interval.