I don't understand how to do the concept, can someone help make it clear!

Whenis unknown and the sample is of sizen30, there are two methods for computing confidence intervals for.

Method 1: Use the Student'stdistribution withd.f.=n1.

This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method.

Method 2: Whenn30, use the sample standard deviationsas an estimate for, and then use the standard normal distribution.

This method is based on the fact that for large samples,sis a fairly good approximation for. Also, for largen, the critical values for the Student'stdistribution approach those of the standard normal distribution.

Consider a random sample of sizen=41, with sample meanx=44.0and sample standard deviations=4.9.

(a) Compute 90%, 95%, and 99% confidence intervals forusing Method 1 with a Student'stdistribution. Round endpoints to two digits after the decimal.

The upper and lower limit of 90%?

The upper and lower limit of 95%?

The upper and lower limit of 99%?

(b) Compute 90%, 95%, and 99% confidence intervals forusing Method 2 with the standard normal distribution. Usesas an estimate for. Round endpoints to two digits after the decimal.

The upper and lower limit of 90%?

The upper and lower limit of 95%?

The upper and lower limit of 99%?

(c) Now consider a sample size of81. Compute 90%, 95%, and 99% confidence intervals forusing Method 1 with a Student'stdistribution. Round endpoints to two digits after the decimal.

The upper and lower limit of 90%?

The upper and lower limit of 95%?

The upper and lower limit of 99%?

(d) Compute 90%, 95%, and 99% confidence intervals forusing Method 2 with the standard normal distribution. Usesas an estimate for. Round endpoints to two digits after the decimal.

The upper and lower limit of 90%?

The upper and lower limit of 95%?

The upper and lower limit of 99%?