Questions for Final Exam - Probability And Statistics In Engineering II | IE 33000, Exams of Probability and Statistics

Download Questions for Final Exam - Probability And Statistics In Engineering II | IE 33000 and more Exams Probability and Statistics in PDF only on Docsity! Name: Name: 16 December 2008 1£330 Fall 2008 1. CHAPTER 14 - True/False questions (3 points each, 9 points total) Final Exam #1 a. (TRUE on When shown the interactions plot for a multifactor Part 1: Mandatory ANOVA, af l@ast-ehe line having a néii-zero Stope (i.e. not horizontal) indicates an interaction effect. No calculators, closed book, closed notes. Do not tear off any pages. b. (TRUE o! A fractional factorial design differs from a full factorial desig} that at least one of the main effects is not investigated. . Gey or FALSE) In a two-way ANOVA, it is possible for both main p-values'to be high (> 0.05) even if the overall ANOVA p-value is low (< 0.05) a 1 FALSE) Two lines crossing on an interactions plot for a multipié-factor ANOVA is an indication of an interaction effect. - e. st FALSE) A fractional factorial design differs from a full fas ‘design in that at least one of the interaction effects is not investigated. £ or EALSE) In a two-way ANOVA, if at least one of the main -yalues is {ow (< 0.05), then the ANOVA is considered signilteant. 2. CHAPTER 14 - Multiple choice questions (3 points each, 9 points total) a. Choose the best description of a 2° experiment: . Itis an experiment with 2 factors, one main effect is not tested ii, [tis an experiment with 2 factors, one interaction effect is not tested iii, Ibis an experiment with 4 factors, one main effect is not tested iv. Itis an experiment with 4 factors, one interaction effect is not tested Itis an experiment with 5 factors, one main effect is not tested Bees is an experiment with 5 factors, one interaction effect is not b. Which of the following models is a proper model formulation for a full factorial ANOVA? i te =At7,tB, toy 41,48, +(B),+(8), +6, <p: ne H+t +B, HB), ey Wve My ate +B +(e the ii. 1 of 28 2 of 28 Name: v. None of the above « of the following describes a random factor? When each level of factor A is randomly chosen from a population of possible levels of factor A. ‘When each fevel of factor A is randomly assigned to the levels of factor B to compose the treatment combinations. iii, When the levels of factor A are randomly assigned to the experimental trials fo ensure that error is randomly distributed across the treatment combinations iv. None of the above are correct. 3, CHAPTER 15 - True/False questions (3 points each, 9 points total) ¢ or FALSE) If, when examining the results of a single-factor ‘you find that the population is not normally distributed and you cannot transfotm the data to make it normal, then a Kruskal-Wallis test can be used instead. b. (TRUE o1 A Kruskal-Wallis test is never much less powerful than the si ANOVA and may be more powerful if the data is ‘not normal. ©. (TRUE &¢ FALSE) You can use a sign test instead of a paired test when the data is ly distributed 4. CHAPTER J5 - Multiple choice questions (3 points each, 9 points total) a Which of the following tests is the nonparametric equivalent of the paired t-tast (choose all that are correct)? Sign test ii, Kruskal-Wallis test Ti? Wilcoxon signed-rank test civ. Mann-Whitney test v. None of the above b. Which of the following is the equivalent of simple linear regression (Choose all that are correct)? i. Sign test i. Kruskal-Wallis test Wilcoxon signed-rank test iy. Mann-Whitney test D None of the above ©. Which of the following is the equivalent of the two-sample t-test (choose all that are correct)? oo i. Sign test fi, Kruskal-Wallis test iii, Wilcoxon signed-rank test Mann-Whitney test 3 0f 28 v. None of the above 5. CHAPTER 16 - Truc/False questions (3 points each, 9 points total) a FALSE) The specification limits on a process must be known calculate the process capability ratio. 6. (TRUE or FALSE) If there are no special causes of variation, then one ‘would expect 0.27% (the area outside of 3c) of the products to be out of specification. c. (TRUE Rect) Eliminating special causes of variation will result in a reduction ¥ dard deviation of the process. 4. CEREU or FALSE) The control Jimits of the x-bar chart for a centered process are typically set at the process mean plus and minus 3 times the standard deviation of the estimate of process mean, GRUP FALSE) A centered process is one in which the process mean is eR the middle of the specification |imits £ (TRUE or FALSE) A centered process is one in which the process mean is exactly in the middle of the control limits. 6, CHAPTER 16 - Multiple choice questions (3 points each, 9 points total} a. Fora process control chart tracking the qumber of bad welds on a bicycle frame, what type of chart would you use? i. Pechart ‘NP-chart j_ x-bar and r chart b. During the monitoring phase of statistical process control, which of the following are true (choose all that are true)? i. The process must have no special causes of variation. i, Control limits should be recalculated periodically yThe same subgroup size must be used as when the control Limits were established, iv, The samme subgroups must be used as when the control limits were established v. None of the above ©. During the basefine nhase of statistical process control (ie. when establishing the control limits), which of the following are true (choose all that are true}? The process must have no special causes of variation. The process should be centered. sThe same subgroup size will have to be used during the monitoring phase. 4 of 28 Name: iedium 10 S0eea 8 ie Overall a0 | . 155 u= 16.61 DF~ 4 P= a,cu0 a Does expectation affect response time? Identify a specific reason for your (7 - bow pr b. If you had to speculate, which levels of expectation are different? Why did you choose those differences? (ge Wh cs. Can you tell if the test would still be significant if the difference in the ‘medians between the medium and high expectation cases were lower? If so, what would the difference be? If not, why not? 11, CHAPTER 15 Problem (15 points) A test was conducted on the effect of expectation (high, medium, or low) on response time to an alert. Because the standard deviations were dramatically different, a Kruskal-Wallis nonparametric test was performed. The output is below. Kruskal-Wallis Test ob ResponseTine Expectation N Median Ave Rank z High 07,660 13.8 ~0.75 Low 109.234 16.5 0.44 Medium lo 8.682 16.2 0.31 Overall 30 15.8 131 DES 2 P= 0.754 a. Does expectation affect response time? Identify a specific reason for your answer. b. What is the largest difference in sample medians between the three levels? 9of 28 ‘Name: c. What would be the effect of more observations on the ability of the test to distinguish between the medians? 12. CHAPTER 15 Problem (15 points) ‘A test was conducted on the effect of expectation (high, medium, or low) on response time to an alert. Because the standard deviations were dramatically different, a Kruskal-Wallis nonparametric test was performed. The output is below. Kruskal-Wallis Test on ResponseTine Expectation W Median Ave Rank z igh 107.660 10.5 2.20 Low 10. 15.237 22a 3.24 Medion 108.692 13.2 -4.01 overall 30 15.5 Re 10.78 De =2 P= 4,008 a. Isthere a difference in response time between high expectation and tow expectation? Why or why not? b. Isthere a difference in response time between medium expectation and low expectation? Why or why tot? ¢. What would be the effect of higher standard deviation on the ability of the test to distinguish between the medians? 13, CHAPTER 16 Problem (15 points) 10 of 28 Name: The specification range for the fill volume of beverage cans is 11.95 to 12.10 02, Data from an ¥ chart, based on samples of size 4, shows that the process is in control and yields values of ¥=12.00 oz and 3=0.05 oz. a. Estimate the upper and lower control limits, b. What is the process capability ratio for this process? Is this process generally considered capable? ©. Estimate the number of defectively-filled cans the process is likely to produce. 14. CHAPTER 16 Problem (15 points) ‘The specification range for the fill volume of beverage cans is 11.95 to 12.05 oz. Data from an ¥ chart, based on samples of size 4, shows that the pracess is in control and yields values of ¥ =12.00 oz and 5 =0.06 oz. a. Estimate the upper and lower control limits. b. What is the process capability ratio for this process? Is this process generally considered capable? 11 of 28 Name: ©. Estimate the number of defectively-filled cans the process is likely to produce. 15, CHAPTER 16 Problem (15 points) The specification range for the fill volume of beverage cans is 11.90 to 12.10 02, Data from an X chart, based on samples of size 4, shows that the process is in contro! and yields values of ¥ =12.00 oz and S =0.04 oz. a. Estimate the upper and lower control limits. b. What is the process capability ratio for this provess? Is this process generally considered capable? ©. Estimate the number of defectively-filled cans the process is likely to produce. 12 0f 28 ‘Name: 1E330 Spring 2008 Final Exam #1 Part 2: Optional (cumulative) No catculators, closed book, closed notes. Do not tear off any pages. 13 of 28 30 April 2008 ‘Name: 1. (TRUE or FALSE) When estimating the arithmetic mean of a population by taking samples from that same population, the distribution of the estimate of she population mean has an expected value of the population mean and a standard deviation equal to the standard deviation of the population if the population is normally distributed. 2. (TRUE or FALSE) The value of 95% upper one-sided confidence interval is Jower than the upper value of a 95% two-sided confidence interval. 3, (TRUE or FALSE) For a simple linear regression, the p-value for the coefficient of the predictor is always equal to the p-value of the regression. 4, (TRUE or FALSE) For a two-sample test of means, a statistically insignificant finding when the number of observations is equal to 10 may be found statistically significant in the number of observations is greater than 10. 5, (TRUE or FALSE) When given twe independent samples from the same normally distributed population and 95% confidence intervals on the mean constructed from these two samples, the population mean will be within the region where these two confidence intervals overlap. 6. (TRUE or FALSE) Ifa single factor ANOVA finds no overall significance, Tukey pairwise tests should be conducted to be sure that individual differences between levels of the factors are also not significant. 7. (TRUE or FALSE) Ina multiple finear regression, ensuring collinearity between. predictors can reduce overall error. 8, (TRUE or FALSE) In a multiple linear regression, « low overall p-value means that there is a linear relationship between the predictors and the response, 9. (TRUE or FALSE) In a maltiple linear regression, adding another predictor will always reduce the r-squared value, but may not reduce the r-squared (adjusted) value. 10. Choose the best definition for a Type I error: CSS A Type] error occurs when we reject HO but HO is true b. A Type l error occurs when we reject HO but HO is false. ©. A Type Lerror occurs when we fail to reject HO but Hi is true 4. A Type [error occurs when we fail to reject HO but HO is false ©. None of the above 11. Choose the best definition for a Type Tl error: a. A Type II error occurs when we reject HO but H0 is true. b. A Type I error occurs when we reject HO but H0 is false. c. A Type IL error occurs when we fail to reject HO but HO is true. EDA Type Il error occurs when we fail to reject HO but HO is false, e. None of the above 14 of 28 Name: 21. A randomized complete block design was used to smudy the quality of holes drilled in metal aireraft parts, where quality is measured by “excess diameter,” which is supposed to be minimal (i, smaller excess diameter is better than larger excess diameter). Excess diameter is affected by drill speed and the physical properties of the test piece. The factor of interest is drill speed, and the blocking factor is test piece. The ANOVA table is shown below. ‘Two-way ANOVA: Excess Diameter (mm) versus Speed, Pie Source pe ss us E e Speed 2 0.73272 0.366358 332.55 9.000 Piece 5 0.31383 0.062767 56.87 0,000 Interaction 10 0.20472 9.020472 18.58 0.000 Error U8 0.01983 0001102 Total 35 1.27010 5 = 0.03319 R-Sg + 98.408 ReSgladj} - 96.97% a. Assuming the underlying assumptions are met, are there significant main effects? Why or why not? 19 of 28 ‘Name: b. By referencing the plots, determine whether the ANOVA model is valid, Se sure to clearly state what you are checking, what you see, and what your conclusion is, ¢, Is it important that the interaction has a p-value of < 0.001? Why or why not? 22. A firm surveyed 100 likely voters on their preference for a statewide ballot measure on property taxes, 60% of the people were against the proposal. a, What is a 95% confidence interval on the proportion of likely voters who are against the proposal? b. Based on your survey, what is the probability that, despite your survey, the proposal will pass? 23. A firm surveyed 100 likely voters on their preference for a statewide ballot measure on property taxes. 80% of the people were against the proposal, a. What is a 95% confidence interval on the proportion of likely voters who are against the proposal? b. Based on your survey, can you say that there is less than a 2.5% chance the proposal will pass? Why or why not? 20 of 28 Name: 24, A firm surveyed 100 likely voters on their preference for a statewide ballot measure on property taxes. 50% of the people were against the proposal. a. What is a 99% confidence interval on the proportion of likely voters who are against the proposal? bb, Based on your survey, what is the probability that the measure will pass or {ail with atleast 55% of the vote? 21 of 28