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Chapter 9: Q4 (page 438)

Degrees of Freedom

For Example 1 on page 431, we used df smaller of n1-1and n2-1, we got , and the corresponding critical values aret=±2.201. If we calculate df using Formula 9-1, we getdf=19.063, and the corresponding critical values are t=±2.201. How is using the critical values of more “conservative” than using the critical values of ±2.093.

Short Answer

Expert verified

The formula used is simpler and less accurate as compared to the formula 9-1.

Step by step solution

01

Given information

The formula used for degree of freedom of mean is:

df=minn1-1,n2-1 , the results are:

df=11, critical valuest=±2.201

The formula used for degree of freedom for comparison of mean is:

df=s12n1+s22n22s12n12n1-1+s22n22n1-1, the results are:

When df=19.63, critical valuest=±2.093

02

Explanation of the statement

The formula used to obtain the critical value 2.093 is obtained accurately:

The simpler formula df=minn1-1,n2-1can be used more easily and flexibly but may not be that accurate to give results.

Hence, the critical value obtained using df=minn1-1,n2-1is more conservative than the ones computed with another formula.

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