ENSE 627 QUALITY MANAGEMENT IN SYSTEMS

Spring 1998

Homework Assignment 7, Due 6:30 pm, April 1, 1998


Chapter 5. Analysis of Data

5.5 Assignment Problems ( Page 5-34, 5-35 )


5.1 A professor, who is teaching a laboratory class, has provided Mr. XYZ, a teaching assistant, with a data sheet. On the sheet, results from the 300 experiments performed by the students during the past three years are listed. He calculated the mean of the 300 data, which equal to 124.0 GPa. The he sorted the data in an ascendant order. He found that 285 of the 300 data range from 104.4 Gpa to 143.6Gpa.
(1) Estimate the standard deviation of the data set under an assumption that a normal distribution is applicable (provide the justifications)
(2) This semester he is in charge of supervisiong the experiments and grading the lab reports. Here is the data set collected from the student lab reports:

134.6 117.6 124.5 105.6 102.4 149.2 138.6 150.1
125.8 117.4 104.3 152.5 149.3 109.3 ???.? 137.5


He calculated the mean which is equal to 128.0 Gpa. Insert the missing data.
(3) Construct the 95% confidence interval to make a judgement on the observation.
(4) Calculate the standard deviation of the data set containing the 16 measurements and use t-distribution, instead of normal distribution, to construct the 95% confidence interval for your judgement.
(5) Compare the two judgements obtained from (2) and (3), what have you learned for making a good judgement?

5.2 As the instructor of this class said, the price for a dozen of large eggs in the Washington, D.C. area obeys a normal distribution. Based on the past three years data, the mean and standard deviation are $1.10 and $0.15, respectively. There has been almost no effect on the price due to inflation. Recently, a student went to 10 local stores and recorded the price for a dozen of large eggs.

Store 1 Store 2 Store 3 Store 4 Store 5 Store 6 Store 7 Store 8 Store 9 Store 10
1.36 1.28 1.05 0.95 1.36 1.40 0.87 1.05 1.10 1.28


Analyze the data and provide your view on the pricing issue.

5.3 On the day before his final examination on ENME ABC, John was reviewing his exam scores during the past hour exams and quizzes. Can you guess what score John received on the final examination of ENME ABC?

Quiz 1 Quiz 2 Exam 1 Quiz 3 Quiz 4 Exam 2 Quiz 5 Quiz 6
75 80 70 85 80 75 65 90


5.4 Mr. John Smith is testing the noise level of two types of sanders. 20 experiments have been performed for each of the tow types of sanders. The recorded data in terms of DB are listed as follows. Let us use two approaches for the comparison.

Sand 1:

51.56 52.43 53.32 52.68 51.98 51.45 52.02 52.42 51.87 53.02
51.34 52.84 51.56 51.87 51.92 52.03 53.03 52.74 1.10 1.28


Sand 2:

51.89 51.65 53.09 51.65 52.93 51.65 51.98 51.36 51.89 52.04
51.67 52.48 52.67 51.98 51.83 53.05 53.28 51.13 53.83 52.34


(1) Calculate the mean and standard deviation of the 20 measurements for each of the two types of sanders and then make a comparison. Based on the results, interpret the observed difference. Comment on your work? Which type is better in terms of the noise level?

(2) Divide the 20 measurements of Sander 1 into tow groups. Calculate the mean and standard deviation of the 10 measurements for each of the tow groups and then make a comparison between the two groups. Based on the results, interpret the difference observed in (1). Comment on your work. Which type is better in terms of the noise level?