Question

1. For a normal population with known variance ? 2 , what are the CI levels for the following intervals:

(a) ?̅− 2.14? √? ≤ ? ≤ ?̅+ 2.14? √?

(b) ?̅− 2.49? √? ≤ ? ≤ ?̅+ 2.49? √?

(c) ?̅− 1.85? √? ≤ ? ≤ ?̅+ 1.85? √? 2.

2.By how much must the sample size n be increased if the length of the CI on ? from the previous question is to become one third the original length(for fixed, given ?)

Answer 1

(a)

From z tale area left to z-score -2.14 is 0.0162. So we have

Therefore required confidence interval level is

Answer: 96.76%

(b)

From z tale area left to z-score -2.49 is 0.0064. So we have

Therefore required confidence interval level is

Answer: 98.72%

(c)

From z tale area left to z-score -1.85 is 0.0322. So we have

Therefore required confidence interval level is

Answer: 93.56%

2:

To reduce the  length of the CI by one third we need to reduce margin of error by 1/6 That is new sample size must be 36 times larger than old sample size. That is new sample size is 36n.