Chapter 10, Problem 4PT

To determine

To choose: The option defining correct difference in the confidence interval

Answer to Problem 4PT

Option A is the correct choice.

Tom will have a wider confidence interval.

Explanation of Solution

Given information:

Sample size (n) $=10$

95% confidence interval constructed by Tom at 9 degree of freedom

95% confidence interval constructed by Janelle at 16.87 degree of freedom

Calculation:

Critical value at 9 degree of freedom

  ${{\displaystyle t}}_{9|\frac{1-0.95}{2}}={{\displaystyle t}}_{9|0.025}=2.262$

Critical value at 16.87 degree of freedom

  ${{\displaystyle t}}_{16.87|\frac{1-0.95}{2}}={{\displaystyle t}}_{16.87|0.025}=2.111$

It can be seen that as the degree of freedom increases, the critical value decreases.

If the critical value decreases, it will lead to a less wide confidence interval.

Hence, the confidence interval at 9 degree of freedom will be wider than the interval constructed at 16.87 degree of freedom.