_{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}
(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 .
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