1 Name: Michael Williams ISYE 3125 – Statistical Quality Control Ch03 – Modeling Process Quality HW2 This HW consists of five questions and is worth 100 points. Please show all work
for problems requiring computations. Posting only the results earns zero points. Problem 3.1 The content of liquid detergent bottles is being analyzed. Twelve bottles, randomly selected from the process, are measured, and the results are as follows (in fluid ounces): 16.05, 16.03, 16.02, 16.04, 16.05, 16.01, 16.02, 16.02, 16.03, 16.01, 16.00, 16.07. A.
Calculate the sample average. (4 pts) (16.05 + 16.03 + 16.02 + 16.04 + 16.05 + 16.01 + 16.02 + 16.02 + 16.03 + 16.01+ 16.00 +16.07)/ 12 = 16.029 B. Calculate the sample standard deviation. (
4 pts) Sample mean = 16.0292 Squared differences:
(16.05
−
16.02916667) ^2
(16.03
−
16.02916667) ^2 (16.02
−
16.02916667) ^2 (16.04
−
16.02916667) ^2 (16.05
−
16.02916667) ^2 (16.01−16.
02916667) ^2 (16.02−16.
02916667) ^2 (16.02−16.
02916667) ^2 (16.03−16.
02916667) ^2 (16.01−16.
02916667) ^2 (16.00
−
16.02916667) ^2 (16.07−16.
02916667) ^2 Variance is SUM OF Squared differences DIVIDED BY 11
Sum of Squared = 0.004651 0.005406 / 11 = 0.0004228 which is the variance
Sample Standard Deviation is the Square root of the variance so √
0.0004505 = 0.020 is Sample Standard deviation
