Homework
I. Use excel sheet to calculate all relevant numbers and graphs.
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Sample #
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Readings on hour#
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1
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2
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3
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4
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5
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6
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1
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253
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250
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249
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247
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252
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248
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2
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249
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246
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248
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248
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249
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253
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3
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245
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255
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247
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253
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249
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251
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4
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249
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247
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252
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252
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249
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254
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5
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244
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243
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254
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250
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248
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253
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6
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253
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247
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250
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250
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244
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252
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7
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246
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249
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248
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253
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247
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247
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8
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248
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249
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250
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250
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251
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253
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9
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251
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256
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245
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254
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252
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249
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10
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253
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247
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252
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248
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250
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246
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11
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246
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246
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245
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249
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249
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249
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12
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249
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250
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252
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254
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252
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257
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13
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251
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249
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250
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254
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249
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253
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14
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252
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252
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251
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249
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247
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243
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15
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247
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251
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246
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252
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251
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253
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What is the UCL for the ??¯ chart based on the data above? The data pertains to the weight in grams of a drum brkae for XYZ branded car. Upper specification limit (USL) for the product is 260 g and lower specification limit (LSL) is 240 g and the target mean is 250 g. Daily production is 25000 units.
i. What is the LCL, UCl and center line for the ??¯ chart for the problem with data given?
ii. What is the UCL, LCL and center line for the R-chart based on the data given?
iii. Chart the data and comment on whether the processis under control?
iv. In general, in an R-chart, the center line will
• always be at the midpoint of LCL and UCL for that chart.
• sometimes be at the midpoint of LCL and UCL.
• never be at the midpoint of LCL and UCL for that chart.
v. In the ??¯ chart for this problem, the center line will
• always be at the midpoint of LCL and UCL .
• sometimes be at the midpoint of LCL and UCL.
• never be at the midpoint of LCL and UCL .
vi. Center line in an ??¯ chart will always be at equidistant from USL and LSL for that product.
• True
• False
vii. Using the data, and using ??? as the best estimate for Mu and Sigma-hat (using the estimation method) as the best estimate for population sigma, what will be Z-value corresponding to USL?
viii. Using data given, what will be proportion of units that will be within the USL and LSL? Be carefule and try to be accurate.
II. Show the population distribution and the distribution of sample mean with a sample size of 25 in the same graph, paying attention to scale as much as possible. Population mean = 300, population s.d. = 16.
III. Suppose that a population of brakes supplied has a mean stopping distance, when the brake is applied fully to a vehicle traveling at 60 mph is 300 feet. This is considered as a "good" lot. Population standard deviation is 25 feet. Suppose that you take a sample of n brakes to test and if the average stopping distance is less than or equal to a critical value, you accept the lot. If it is more than the critical value, you reject the lot. You want an alpha of 0.05. Further, we want to reject lots with a population mean stopping distance of 320 ft. (mean of the "bad" lots) , we want to reject with a probability of 0.9. (Note that it is one sided, since we would not get worried if the vehicle stops at a distance shorter than the average time.)
i. Draw a diagram and mark the two distributions, alpha, beta and CV.
ii. What is the correct sample size that can achieve this?
iii. What is the critical value?
IV. Population A: 40% male and 60% female and both groups have similar interest in the preference for a policy of interest, that we are trying to measure.
Population B: 30% over 60 years of age; 50% between 30-60 and 20% between 18-30. Over 60 has very divergent preferences for a policy of interest, 30-60 has some variation and 18-30 has very little variation.
You are going to sample the populations to find a measure of interest in some characteristic. (example : preference for making college free).
i. In which population you think stratified sampling will have maximum benefit? Why?
ii. Suppose you are sampling 100 people from population B, which sub-population will get disproportionate number of samples under stratified sampling? Why?
V. A quality engineer in a light bulb factory is planning a study to estimate the average life of a large shipment of light bulbs. The engineer wants to estimate with 92 percent confidence level. Assuming that process standard deviation of 25 hours, he/she found the sample size to be 64. The quality analyst forgot the error allowed used in the calculations. Can you find the error number used in the calculations?
VI. Length of a confidence intervals for a population parameter, such as mean, is defined as the higher value - lower value. Example, if [3,7], the range is 7-3=4. In general answer thje following assuming other things remain the same,
i. As sample size (n) decreases, Length of the interval will become smaller. True or False;
Justify
ii. As confidence level increases, length of the interval will become smaller. True or False;
Justify
iii. As mean shifts by 8 units, (population s.d. remains the same) , no effect will be seen in the length of the interval. True or False; Justify
VII. Explain how you will estimate the process capability, (Remember the formula for Cpk from ch 9) If you are given ??¯ , sample size, center line for the mean, USL and LSL. Use your own numbers to illustrate the calculations. (hint: d2 is used).
Format your homework according to the following formatting requirements:
o The answer should be typed, using Times New Roman font (size 12), double spaced, with one-inch margins on all sides.
o The response also includes a cover page containing the title of the homework, the student's name, the course title, and the date. The cover page is not included in the required page length.
o Also include a reference page. The Citations and references must follow APA format. The reference page is not included in the required page length.