Question

5. A nurse at a drive-up virus check point collected the following service times (in minutes) for 20 randomly selected customers broken into 4 samples. Sample 2 4.6 4.5 Sample 3 4.5 4.6 Sample 1 4.5 4.2 4.2 4.3 4.3 Sample 4 4.7 4.6 4.8 4.5 4.9 4.7 4.3 4.4 4.6 A. Determine the mean of each sample. B. If the drive-up process parameters are unknown, estimate its mean (grand mean) and overall sample standard deviation for the process (20 observations). C. Now, estimate the mean and standard deviation of the sampling distribution (Hint: n = 5). D. What would 3-sigma control limits for the means of the process be? E. Given limits of 4.14 and 4.86, are any sample means beyond the control limits? If so, which one (s)?

Answer 1

a)

	Sample 1	Sample 2	Sample 3	Sample 4
	4.5	4.6	4.5	4.7
	4.2	4.5	4.6	4.6
	4.2	4.4	4.4	4.8
	4.3	4.7	4.4	4.5
	4.3	4.3	4.6	4.9
Mean	4.3	4.5	4.5	4.7

b)

Grand Mean	4.5
Standard Deviation	0.180278

c)

	Sample 1	Sample 2	Sample 3	Sample 4
	4.5	4.6	4.5	4.7
	4.2	4.5	4.6	4.6
	4.2	4.4	4.4	4.8
	4.3	4.7	4.4	4.5
	4.3	4.3	4.6	4.9
Mean	4.3	4.5	4.5	4.7
Std dev	0.1	0.129099	0.08165	0.129099

d)

	Sample 1	Sample 2	Sample 3	Sample 4
	4.5	4.6	4.5	4.7
	4.2	4.5	4.6	4.6
	4.2	4.4	4.4	4.8
	4.3	4.7	4.4	4.5
	4.3	4.3	4.6	4.9
Mean	4.3	4.5	4.5	4.7
Std dev	0.1	0.129099	0.08165	0.129099
3 sigma (Upper)	4.6	4.887298	4.744949	5.087298
3 sigma (Lower)	4	4.112702	4.255051	4.312702

e) One sample is outside in sample 4