Question

Is a 99% confidence interval with n=50 a better chance of capturing the populations mean height or is a 90% confidence interval with n=100 a better chance?

Answer 1

Looks like you'll need to calculate the margin of error for each case, and then compare them. The situation that results in a smaller margin of error has the better chance of 'capturing" the mean height.

Hints: For a 99% confidence interval, the z critical value is 2.575 (better check this for accuracy!!); for a 90% conf. int., the z critical value is 1.645.

More hints: use S as the standard deviation in both cases.
Then, for a sample of 50, the sample standard deviation is S/Sqrt(50); for a sample of 100, the sample s. d. is S/Sqrt(100).

The Margin of Error is calculated as follows:\[(z-critical-value)*\frac{ S }{ \sqrt{n} }\]

Answer 2

Awesome thanks :)

Answer 3

My pleasure!!