1. South Dakota School of Mines & Technology Estimation Industrial Engineering

2. Estimation Interval Estimates Industrial Engineering

3. Interval Estimates
Suppose we wish to determine if the mean gpa for women is higher than it is for men. We know that

4. Interval Estimates
It stands to reason that if the mean gpa for women is normally distributed and the mean gpa for men is normally distributed, the random variable D = is normally distributed. Further

5. Interval Estimates
Further, if
then

6. Interval Estimates ) ( 1 z Z P £ - =
Recall that for a standard normal distribution,
za/2
za/2
a/2
1 - a ) ( 1 2 / a z Z P - =

7. Interval Estimates
Then,

8. Interval Estimates
A 1-a confidence interval is then given by

9. Interval Estimates
Suppose a sample of 10 women and 20 men yields a sample mean gpa of 2.92 for women and a sample mean gpa of 2.85 for men. We know from past data that the standard gpa for both women and men is Is there evidence to believe women do better than men at the 90% confidence level?

10. Interval Estimates

11. Interval Estimates
Suppose a sample of 10 women and 20 men yields a sample mean gpa of 2.92 for women and a sample mean gpa of 2.85 for men. Further, suppose that we estimate the variance for women at 0.08 and the variance for men at Is there evidence to indicate that women do better academically than men?

12. Interval Estimates
It’s straightforward that with variance unknown we, switch to the T distribution with a pooled variance. Then, A 1-a confidence interval is then given by

13. Interval Estimates
For our problem then, we have