Assume that a sample is used to estimate a population mean u. Find the 99% confidence interval for a sample of size 68 with a mean of 36.2 and a standard deviation of 18.9. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places.

Obtain the 99% confidence interval to estimate the population mean.

The 99% confidence interval to estimate the population mean is obtained below:

The formula for the Confidence interval for mean is:

Obtain the degrees of freedom.

The degrees of freedom is obtained below:

Use EXCEL Procedure for finding the critical value of t.

Follow the instruction to obtain the critical value of t:

1. Open EXCEL
2. Go to Formula bar.
3. In formula bar enter the function as“=TINV”
4. Enter the probability as 0.01.
5. Enter the degrees of freedom as 67.
6. Click enter

EXCEL output:

From the EXCEL output, the critical value of t at 0.01 level of significance with the 67 degrees of freedom is 2.6512.