Question

An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 1.7 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 of​ confidence, does it seem likely that the population mean could be within 10% of the sample​ mean? within 11​% of the sample​ mean? Explain.

Answer 1

a)

	for90% CI crtiical Z          =	1.645
	standard deviation σ=	1.8
	margin of error E =	1.7
required sample size n=(zσ/E)2                  =		4

b)

Yes since 10% of the sample mean is 20*0.1 =2 which is less than margin of error, therefore it seem  likely that the population mean could be within 10% of the sample​ mean and also within 11​% of the sample​ mean