Final Exam - Spring ST 370 Online - A

Transcription

1 Final Exam - Spring ST 370 Online - A Darken the circle on the answer sheet corresponding to your answer. Use a number 2 pencil. Stray marks on the form may cause errors. All questions are worth 3 points. 1. An important distinction in the second half of the course is between discrete and continuous random variables. Which one of the following types is a discrete random variable? A. normal B. binomial C. Weibull D. exponential 2. The 67th percentile is A. the point such that 33 percent of the data lies below it B. close to the standard deviation C. the point such that 67 percent of the data lies below it D. close to the interquartile range 3. Which of the following are measures of variability (or dispersion)? A. standard deviation B. sample range C. interquartile range D. All of the above 4. The probability that a standard normal random variable Z lies above 1.44 is given by A B C D Suppose that a small sample is given by 3.56, 2.78, 1.24, The sample standard deviation is A B C D

2 6. In the early lesson on hypothesis testing, the following statement was found in the summary (talking about comparing two population mean values): The p value is a useful measure of evidence against the null hypothesis. But one must be careful because a small p value can be due to either (i) a large population mean difference and small sample sizes or (ii) a small population mean difference and large sample sizes. For which of those two situations would we say we have a statistically significant result but not likely a practically significant result? A. (i) B. (ii) 7. When is Pr(A or B) = Pr(A)+ Pr(B)? A. Always. B. Never. C. Only when A and B are statistically independent events. D. Only when A and B are mutually exclusive events. 8. When is Pr(A and B) = Pr(A)Pr(B)? A. Always. B. Never. C. Only when A and B are statistically independent events. D. Only when A and B are mutually exclusive events. 9. We are studying a population with unknown mean µ and standard deviation that we guess is around 3. We plan to take a random sample and want to construct a 95% confidence interval of length 2 (right endpoint left endpoint = 2). How large should the sample size be? A. 24 B. 6 C. 16 D True or False: If the same data are used for both intervals, a 95% confidence interval for π is always wider than a 90% confidence interval for π. A. True. B. False. 2

3 11. A survey has discovered that the amount of money that a family of four spends on food per week is approximately normally distributed and has a mean of $100 and a standard deviation of $12. What proportion of families spend between $80 and $110 per week on food? A B C D For the previous problem, what is the 99th percentile (to the nearest dollar)? A. $131 B. $128 C. $124 D. $120 The next three questions relate to the following situation. Items are randomly pulled off an assembly line and measured. In a 4 hour period the values are 21.1, 20.4, 22.5, 22.6, 23.5, 22.8, 24.2 The target value is 21.0, and the process engineer wants to test at α =.05 whether the process mean is 21.0 or different from From matlab, the sample mean and sample standard deviation are and 1.31, respectively. 13. The correct pair of hypotheses is A. H 0 : µ =21.0 vs.h 1 : µ 21.0 B. H 0 : µ 21.0 vs.h 1 : µ<21.0 C. H 0 : µ 21.0 vs.h 1 : µ>21.0 D. None of the above 14. The test statistic to be used is A. (P 21.0)/ P (1 P )/n B. (X 21.0)/σ C. (X 21.0)/[s/ n] D. (X 21.0)/[σ/ n] 15. Alternatively, one could give a 90% confidence interval for the process mean and see if 21.0 lies in the interval. This interval is A. (22.11,22.77) B. (21.66,23.22) C. (20.10,24.78) D. (21.48,23.40) 3

4 16. Suppose that a certain random variable X has density function f(x) =c(1 x) for 0 <x<1 and f(x) = 0 otherwise. What must the constant c be? A. 1 B. 2 C. 3 D A primary goal of hypothesis testing in ANOVA is to A. use the correct method of randomization. B. find estimates of the overall mean. C. to decide between hypotheses about sample means. D. to decide between hypotheses about population means. The next two questions relate to the following printout from a MATLAB least squares fit of Y versus x: R-square Standard Error Parameter Estimates Source Parameter Estimate Std. Error t p-val Intercept x The least squares equation is A. Y = Z x B. Y = x C. Y = x D. Y = x 19. The the proportion of variation in Y explained by the least squares line (to two decimal places) is A B C D

5 X2=Shampoo X2=Oil X2=Water hot Room Cold X1 Level The next three questions relate to an experiment to study the effect of temperature on the viscosity of three liquids. Viscosity was measured by the time it took for the liquids to drain out of a container. >> viewdata(viscosity) Obs liquid temp time Obs liquid temp time 1 Shampoo hot Oil Cold Shampoo Room Oil hot Shampoo Cold Oil Room Shampoo hot Oil Cold Shampoo Room Water hot Shampoo Cold Water Room Shampoo hot Water Cold Shampoo Room Water hot Shampoo Cold Water Room Oil hot Water Cold Oil Room Water hot Oil Cold Water Room Oil hot Water Cold Oil Room The factors are A. liquid and temperature B. Shampoo, Oil, and Water C. time and viscosity D. hot, Cold, and Room 5

6 21. The response variable is A. liquid B. temperature C. time D. Shampoo 22. From the mplot it appears that A. there is an interaction between the factors. B. water is not affected by temperature. C. the liquids have different viscosities for Room temperature. D. All of the above. The next three questions relate to the following situation. A Dept. of Transportation directive is to resurface roads in a certain area if the proportion of 1000 foot lengths of pavement with major potholes (diameter = 1 foot) is more than 10%. A sample of 100 lengths are made and 18 are found to have major potholes. Thus the hypotheses are H 0 : π.10 vs. H 1 : π> What is the form of the test statistic? A. Z =(.18.10)/ (.10)(.90)/100 B. Z =(.10.18)/σ/ (.18)(.82)/100 C. t =(X.10)/s/ 100 D. t =(X.18)/s/ What is the form of the rejection region for an α =.01 level test? A. Z< 2.05 B. t>2.58 C. t< 2.33 D. Z> Give a 98% confidence interval for the true proportion of lengths of pavement with major potholes. A. (0.06,0.14) B. (0.11,0.25) C. (0.09,0.27) D. (0.08,0.12) 6

7 26. A certain population has mean µ =36.1 and standard deviation σ =3.2. A random sample of n = 20 observations is taken. What is the standard deviation of the sample mean X? A B C. 3.2 D A manufacturing process produces items with major defects only 5% of the time. If 20 items are randomly selected, what is the probability that two or more of the items will have major defects? A B C D An audio system contains 25 components. The probability that any component is defective is 0.02, and all components are independent. The audio system operates only if there are no defective components. What is the probability that the audio system operates (rounded to 2 decimal places)? A B C D Suppose that the body weight the Carolina Hurricane team members is symmetrically distributed. A random sample of the team members weights has a sample mean X = 200 lbs. and a sample standard deviation s = 20 lbs. Approximately 95% of the team members weights should lie within which interval? A. (140, 260) B. (160, 240) C. (180, 220) D. (190, 210) 30. Suppose that X is a continuous random variable? Which of the following must be true? A. Pr(X x) =Pr(X <x) B. Pr(X >x)=1 Pr(X x) C. Pr(X =2)=0 D. All of the above. 7

8 31. Students often have a problem understanding the meaning of an interaction between two factors. Consider the following two sets of means: (i) B (ii) B Level 1 Level 2 Level 1 Level Level Level A A Level Level Which, if any, of (i) and (ii) illustrate an interaction btween factors A and B? A. (i) B. (ii) C. (i) and (ii) D. Neither (i) nor (ii). 32. A continuous random variable X has density function f(x) =x/50 for 0 <x<10 and f(x) =0 otherwise. Then mean of X is A B C D A set of hypotheses about an unknown mean µ is given by H 0 : µ 2 versus H 1 : µ<2. We plan to use a t statistic based on a sample of size n = 4 and significance level α =.10. What is the proper rejection region? A. t>1.533 B. t<2.353 C. t< D. t<