Following are two confidence interval estimates of the mean

Following are two confidence interval estimates of the mean µ of the cycles to failure of an automotive door latch mechanism (the test was conducted at an elevated stress level to accelerate the failure).

3124.9 µ 3215.7                                                       3110.5 µ 3230.1

(a) What is the value of the sample mean cycles to failure?

(b) The confidence level for one of these CIs is 95% and the confidence level for the other is 99%. Both CIs are calculated from the same sample data. Which is the 95% CI? Explain why.

Solution

3124.9 µ 3215.7
3110.5 µ 3230.1

M.E = 3215.7- 3124.9/2 = 45.4
& M.E = 3230.1 - 3110.5/2 = 59.8

a) The Sample Mean = 3124.9+45.4=3170.3
b)
Eqn 1 is 95% c.I & the second os 99%, since 99% gives more wider interval