Answer to Question 1 in Comparison of Means

Question

Question 1. Assume that in different time periods 4 randomly selected patients rated their satisfaction with our services as follows: Download► Answer

Time Period	Rating of 1st Patient	Rating of 2nd Patient	Rating of 3rd Patient	Rating of 4th Patient
1	80	84	82	80
2	70	72	74	70
3	76	78	76	78
4	80			80

Answer

To answer this question we need to calculate the control limits for each time period. First calculate the average for each time period. Second, the average of all observations. Third, the standard deviation of all observations. Finally fourth, calculate the standard deviation for each time period. Now, you are ready to calculate the Upper and Lower control limits. The formula for these calculations and the resulting findings are given below:

Cell	Formula
F2	=average(B2:E2)
G3	=F$7/SQRT(COUNT(B3:E3))
F6	=AVERAGE(B2:E5)
F7	=STDEV(B2:E5)
H2	=F$6-1.96*G2
I2	=F$6+1.96*G2

Then you can plot the control limits and the observations. Note that the UCL and LCL are drawn without markers and in red. Note how the UCL and LCL for the 4th time period is wider than other time periods. This is because there are only 2 observations in this time period and therefore we have a larger standard deviation. Also note that the 2nd time period falls below the control limits showing that in this time period we did worse than usual.