The Chair of the Operations Management Department at Quality University wants to construct a p-chart for determining whether the four instructors teaching the basic P/OM course are under control with regard to the number of students who fail the course.Accordingly,he sampled 100 final grades from last year for each instructor,with the following results: What are the .95 (5% alpha risk)upper and lower control limits for the p-chart?
A).95 and .05
B).13 and .07
C).1588 and .0412
D).16 and .04
E).1774 and .0226

Question

The Chair of the Operations Management Department at Quality University wants to construct a p-chart for determining whether the four instructors teaching the basic P/OM course are under control with regard to the number of students who fail the course.Accordingly,he sampled 100 final grades from last year for each instructor,with the following results:  What are the .95 (5% alpha risk)upper and lower control limits for the p-chart?
A).95 and .05 
B).13 and .07 
C).1588 and .0412 
D).16 and .04 
E).1774 and .0226

Quizplus · Accepted Answer

To construct a p-chart, we first need to calculate the proportion of failures (p) for each instructor. Then, we can calculate the overall proportion of failures (p-bar) and use it to calculate the centerline and control limits.

The formulas for p and p-bar are:

p = number of failures / sample size 
p-bar = (sum of failures for all instructors) / (total sample size)

Using the data provided, we can calculate:

p1 = 10/100 = 0.1 
p2 = 8/100 = 0.08 
p3 = 12/100 = 0.12 
p4 = 15/100 = 0.15

p-bar = (10+8+12+15)/(4*100) = 0.1125

The centerline for the p-chart is p-bar, and the upper and lower control limits can be calculated using the following formulas:

UCL = p-bar + 3*sqrt(p-bar*(1-p-bar)/n) 
LCL = p-bar - 3*sqrt(p-bar*(1-p-bar)/n)

Where n is the total sample size (400).

Plugging in the values, we get:

UCL = 0.15995 
LCL = 0.03905

Therefore, the answer is D: 16 and 0.04 are the upper and lower control limits for the p-chart with a 0.05 alpha risk.