Question

Suppose you wish to estimate a population mean correct to within 0.15 with a confidence level of .90. You do not know sigma squared σ2​, but you know that the observations will range in value between 32 and 40. Complete parts a and b.

a. Find the approximate sample size that will produce the desired accuracy of the estimate. You wish to be conservative to ensure that the sample size will be ample for achieving the desired accuracy of the estimate.​ (Hint: assume that the range of the observations will equal

4sigmaσ​.)

(Round up to the nearest​ integer.)

b. Calculate the approximate sample​ size, making the less conservative assumption that the range of the observations is equal to

6sigmaσ.

​(Round up to the nearest​ integer.)

Answer 1

a)

approximate σ =range/4 =(40-32)/4 =2

	for90% CI crtiical Z          =	1.645
	standard deviation σ=	2
	margin of error E =	0.15
required sample size n=(zσ/E)2                  =		482.0

( please try 481 if this comes wrong)

b)

approximate σ =range/4 =(40-32)/6 =1.3333

	for90% CI crtiical Z          =	1.645
	standard deviation σ=	1.3333
	margin of error E =	0.15
required sample size n=(zσ/E)2                  =		214.0