Question

a random sample of 40 transmission replavement costs find the mean to be $2520.00. Assume the population standard deviation is $400.00. A 95% confidence interval for the population mean repair cost is (2396.0,2644.0)
Change the sample to n=80. Construct a 95% confidence interval for the population mean repair cost. which confidence interval its wider?

Answer 1

Solution:

Given,

When n=40 the confidence interval was (2396.0,2644.0)

Now we put n=80 and find the confidence interval using the formula,

Putting all the values we have,

Upper confidence limit as,

Lower confidence limit as,

Thus the new confidence intervals are (2432,2608)..........(when n=80)

The previous confidence intervals were(2396,2644)..........(when n=40)

Confidence width when n=80 is 2608-2432=176.

Confidence width when n=40 is 2644-2396=248.

Thus when n=40 the confidence interval was wider than when n=80.