STAT 245 Lecture Notes - Lecture 7: Quality Control, Simple Random Sample, Confidence Interval
STAT 245 – Exercises #7
Solutions
PROBLEM A: A company that manufactures custom jackets for groups such as sports teams is so busy
that it operates both a day shift and an evening shift. Quality control is a concern to the company, and it
wanted to compare the two shifts to determine whether or not there was a difference in the proportions
of jackets having defects between the two shifts. Independent random samples of jackets from the
production of each shift over a one-week period were obtained with the following information collected.
Shift
Number of jackets sampled
Number with defects
Day
200
9
Evening
150
12
1. Determine a 95% confidence interval for the difference in the proportions of defective jackets
being produced by the two shifts.
The confidence interval for the difference in the two population proportions is
Where
,
And
,
Also,
Thus, the confidence interval for is
