Question

A new president at Big State University has made student satisfaction with the enrollment and registration process one of her highest priorities. Students must see an advisor, sign up for classes, obtain a parting permit, pay tuition and fees, and buy textbooks and other supplies. During one registration period, 10 students every hour are sampled and asked about satisfaction with each of these areas. Twelve different groups of students were sampled, and the number in each group who had at least one complaint as follows: 0, 2, 1, 0, 0, 1, 3, 0, 1, 2, 2, 0, Develop upper and lower control limits (99.7%) for the proportion of students with complaints. Is the president happy with the results? Explain fully

Answer 1

To find the control limits of the p-chart, we first find the average proportion of complaints. To find this this we find the proportion of complaints in each sample and then find the average

Proportion of complaint in each sample is given by the number of complaints divided by the sample size.

Proportion of complaints in Sample 1 = 0/10 = 0
Proportion of complaints in Sample 2 = 2/10 = 0.2
Proportion of complaints in Sample 3 = 1/10 = 0.1
Proportion of complaints in Sample 4 = 0/10 = 0
Proportion of complaints in Sample 5 = 0/10 = 0
Proportion of complaints in Sample 6 = 1/10 = 0.1
Proportion of complaints in Sample 7 = 3/10 = 0.3
Proportion of complaints in Sample 8 = 0/10 = 0
Proportion of complaints in Sample 9 = 1/10 = 0.1
Proportion of complaints in Sample 10 = 2/10 = 0.2
Proportion of complaints in Sample 11 = 2/10 = 0.2
Proportion of complaints in Sample 12 = 0/10 = 0

is then the average of above proportion = (0+0.2+0.1+0+0+0.1+0.3+0+0.1+0.2+0.2+0)/12 = 1.2/12 = 0.1

We then find the for the given data using the formula below

where n is the sample size = 10. Hence we have the below

The control limits are then calculated using the below formula. If for LCL the control limit come as negative using the formula it is taken as 0 as proportions cannot be negative.

UCL = + z*

LCL =   - z*

where z=3 for 99.7% control limit. Hence we have the control limits as below

UCL = 0.1+3*0.0949 = 0.385

LCL = 0.1-3*0.0949 = -0.185. As LCL is coming negative, it is taken as 0

Hence the final control limits are as below

Lower Control Limit LCL = 0

Upper Control Limit UCL = 0.385

The president would be happy with the results as all the sample proportion calculated previously lie within the control limits calculated above