Question

_{Assume a normal distribution with known population variance. Calculate the lower
confidence limit (LCL) and upper confidence limit (UCL) for each of the following.
a. ?̅ = 50; n = 64; ? = 40; α = 0.05
b. ?̅ = 85; n = 225; ?2 = 400; α = 0.01
c. ?̅ = 510; n = 485; ? = 50; α = 0.10}

Answer 1

(1- )% is the confidence interval for population mean

C.V. =

This value is found using normal percentages tables

In b. We have Var = ?2 = 400 therefore SD = ? = 20 since it is square of variance

	Critival value at	Margin of error	Lower L.	Upper L.
a. ?̅ = 50; n = 64; ? = 40; α = 0.05	1.9600	9.7998	40.2002	59.7998
b. ?̅ = 85; n = 225; ? = 20; α = 0.01	2.5758	3.4344	81.5656	88.4344
c. ?̅ = 510; n = 485; ? = 50; α = 0.10	1.6449	3.7344	506.2656	513.7344

We can see that at large sample sizes the margin of error reduces.

Confidence interval provides range for population paramters with certain probabilties. The higher the probability the width is more to incorporate all the possible values. The higher the sample size the smaller the sample size since more accuracy is possible .