Question

10) Suppose that you are asked to use a sample of size 50 to create a 95% confidence interval for a population mean. The lower limit of your interval turns out to be L and the upper limit turns out to be U. If you were to change the confidence level to 90% and use the same sample data to create a revised confidence interval, would it be correct to say that the revised interval would have a lower limit less than Land an upper limit greater than U? A) Definitely correct B) Definitely incorrect C) Might be correct, might be incorrect, depending on the value of the t statistic for this problem D) Might be correct, might be incorrect, depending on the p-value for this problem E) Is correct, but only if the underlying population is normally distributed

Answer 1

The CI for population mean( for n>30) is given by:

  

Now, when we create 95% confidence interval we have $Z(\alpha /2)$ = 1.96 , and when we create 90% confidence interval   $Z(\alpha /2)$ =1.64, hence the first CI will be wider and the second will be narrower.

Hence when we create 90% CI, the lower limit will be greater than L, and the upper limit will be less than U because now we are adding and subtracting 1.64 instead of 1.96.

Hence the answer will be:

• B.) Definitely incorrect