Question

Two analysts are going to compute confidence intervals for the unknown population mean lifetime of batteries being used in a particular brand of cellphones. The 1st analyst selects a random sample of batteries and computes a 95% confidence interval that has a margin of error of .85 hours. The 2nd analyst selects a random sample of batteries and computes a 99% confidence interval that has a margin of error of .70 hours. Both samples have the same standard deviation of 4 hours. Which analyst will have a wider interval

Answer 1

Due to the higher margin of error, the 1st analyst will have a wider interval.

Explanation:

Width of a confidence interval:

The width of a confidence interval is twice its margin of error, meaning that the sample with the largets margin of error will be wider.

1st analyst:

Margin of error of 0.85, so width of 0.85*2 = 1.7

2nd analyst:

Margin of error of 0.7, so width of 0.7*2 = 1.4

Which analyst will have a wider interval?

Due to the higher margin of error, the 1st analyst will have a wider interval.