Decision Sciences LeBow College of Business Drexel University 3220 Market Street Philadelphia, PA 19104 STAT 201 - Business Statistics I Final Name (Last, First) : Student ID Card# : Part I. T/F Questions (2 points each) (T/F) 1. In a simple regression, there are n - 1 degrees of freedom associated with the error sum of squares (SSE). (T/F) 2. The coefficient of determination is the percentage of the total variation in the response variable Y that is explained by the predictor X. (T/F) 3. If R2 =.36 in the model of Sales = 268 + 7.37 Ads, then Ads explains 36 percent of the variation in Sales. (T/F) 4. The ordinary least squares regression line always passes through the point (, ). (T/F) 5. If SSR is 1800 and SSE is 200, then R2 =.90. (T/F) 6. The total sum of squares (SST) will never exceed the regression sum of squares (SSR). (T/F) 7. If arrivals follow a Poisson distribution, waiting times follow the exponential distribution. (T/F) 8. For a continuous random variable, the total area beneath the PDF must be one. (T/F) 9. The exponential distribution describes the number of arrivals per unit of time. (T/F) 10. The second quartile is the same as median. (T/F) 11. A trimmed mean may be preferable to a mean when a data set has extreme values. (T/F) 12. Given the data set 10, 5, 2, 6, 3, 4, 20, the median value is 5. (T/F) 13. In calculating the sample variance, the sum of the squared deviations around the mean is divided by n - 1. (T/F) 14. The probability of the union of two events P(A or B) can exceed one. (T/F) 15. Independent events are mutually exclusive. Part II. Multiple Choice Questions (1.5 points each) 1. In a sample of 10,000 observations from a normal population, how many would you expect to lie beyond three standard deviations of the mean? a. None of them. b. About 27. c. About 100. d. About 127. 2. On a randomly chosen Wednesday, which probability model would you use to describe the number of convenience store robberies in Philadelphia? a. Binomial b. Poisson c. Hypergeometric d. Geometric 3. Which of the following is not a requirement of a binomial distribution? a. constant probability of success b. only two possible Bernoulli outcomes c. fixed number of trials d. equally likely outcomes. 4.The time required for a citizen to complete the 2010 U.S. Census \"long\" form is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes. What proportion of the citizens will require less than one hour? a. 0.4772 b. 0.9772 c. 0.9974 d. 0.9997 5. The random variable X is normally distributed with mean of 80 and variance of 36. The 67th percentile of the distribution is: a. 72.00 b. 95.84 c. 90.00 d. 82.64 6. A large number of applicants for admission to graduate study in business are given an aptitude test. Scores are normally distributed with a mean of 460 and standard deviation of 80. The top 2.5 percent of the applicants would have a score of at least (choose the nearest integer): a. 606 b. 617 c. 600 d. 646 7. A die is rolled. If it rolls to a 1, 2, or 3 you win $2. If it rolls to a 4, 5, or 6 you lose $1. Find the expected winnings. a. $0.50 b. $3.00 c. $1.50 d. $1.00 8. A machine dispenses water into a glass. Assuming that the amount of water dispensed follows a continuous uniform distribution from 10 ounces to 16 ounces, what is the probability that 13 or more ounces will be dispensed in a given glass? a. 0.1666 b. 0.3333 c. 0.5000 d. 0.6666 9. The lengths of brook trout caught in a certain Colorado stream are normally distributed with a mean of 14 inches and a standard deviation of 3 inches. What proportion of brook trout caught will be between 12 and 18 inches in length? a. 0.6563 b. 0.6826 c. 0.2486 d. 0.4082 10. A student's grade on an examination was transformed to a z value of 0.67. Assuming a normal distribution, we know that she scored approximately in the top: a. 15 percent b. 50 percent c. 40 percent d. 25 percent Final, Business Statistics I 2 11. The standard deviation of a normal random variable X is $20. Given that P(X $10) = 0.1841. From this we can determine that the mean of the distribution is equal to: a. $13 b. $26 c. $20 d. $28 12. Half of a set of the parts are manufactured by machine A and half by machine B. Five percent of all the parts are defective. Two percent of the parts manufactured on machine A are defective. Find the probability that a part was manufactured on machine A, given that the part is defective. a. 10% b. 20% c. 30% d. 40% 13. What does it mean when you calculate a 95% confidence interval? a. The process you used will capture the true parameter 95% of the time in the long run b. You can be \"95% confident\" that your interval will include the population parameter c. You can be \"5% confident\" that your interval will not include the population parameter d. All of the above statements are true 14. What would happen (other things equal) to a confidence interval if you calculated a 99 percent confidence interval rather than a 95 percent confidence interval? a. It will be narrower b. It will not change c. The sample size will increase d. It will become wider 15. A ______ is a subset of a _________. a. Sample, population b. Population, sample c. Statistic, parameter d. Parameter, statistic 16. A _______ is a numerical characteristic of a sample and a ______ is a numerical characteristic of a population. a. Sample, population b. Population, sample c. Statistic, parameter d. Parameter, statistic 17. _____ results if you fail to reject the null hypothesis when the null hypothesis is actually false. a. Type I error b. Type II error c. Type III error d. Type IV error 18. A ________ is a range of numbers inferred from the sample that has a certain probability of including the population parameter over the long run. a. Hypothesis b. Lower limit c. Confidence interval d. Probability limit 19. When the researcher rejects a true null hypothesis, a ____ error occurs. a. Type I b. Type A Final, Business Statistics I 3 c. Type II d. Type B 20. As sample size goes up, what tends to happen to 95% confidence intervals? a. They become more precise b. They become more narrow c. They become wider d. Both a and b Part III. General Word Problems (40 points total) 1. (10 points) A sample of 49 sales receipts from Apple store has the sample mean of $450 and population standard deviation of $70. Use these values to test whether or not the mean of sales at the Apple store would be different from $430. (a) (3 pts) Find 95% Confidence Interval for a mean. (b) (7 pts) Hypothesis Testing with significance level = 0.05. - Step 1. State the null and alternative hypotheses. - Step 2. State Decision Rule for both p-value and critical value methods o Decision Rule for p-value method o Decision Rule for Critical Value Method - Step 3. Find Test Statistic. - Step 4. Conclusion i. By p-value method ii. By critical value method Final, Business Statistics I 4 2. (15 points) Suppose that the relationship between the independent variable x (meaning height) and dependent variable y (meaning weight) is described by a simple linear regression model with true regression line: y = 7 + 0.5x, and = 3. (a) (3 pts) If x = 20, what is the expected value of Y? (b) (6 pts) If x = 20, what is P(Y = 17)? (c) (6 pts) If x = 20, what is P(Y < 23)? 3. (15 points) A sample of data is as follows. Find the 90% confidence interval for a mean. 7, 6, 7, 8, 4, 9, 5, 8, 9 Final, Business Statistics I 5 t-Distribution Table t The shaded area is equal to for t = t . df t.100 t.050 t.025 t.010 t.005 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 1 3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310 1.309 1.307 1.306 1.304 1.282 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.694 1.691 1.688 1.686 1.645 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.037 2.032 2.028 2.024 1.960 31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.449 2.441 2.434 2.429 2.326 63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.738 2.728 2.719 2.712 2.576 Final, Business Statistics I 6 Standard Normal Probabilities Table entry Table entry for z is the area under the standard normal curve to the left of z. z z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 -3.4 -3.3 -3.2 -3.1 -3.0 -2.9 -2.8 -2.7 -2.6 -2.5 -2.4 -2.3 -2.2 -2.1 -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 -0.0 .0003 .0005 .0007 .0010 .0013 .0019 .0026 .0035 .0047 .0062 .0082 .0107 .0139 .0179 .0228 .0287 .0359 .0446 .0548 .0668 .0808 .0968 .1151 .1357 .1587 .1841 .2119 .2420 .2743 .3085 .3446 .3821 .4207 .4602 .5000 .0003 .0005 .0007 .0009 .0013 .0018 .0025 .0034 .0045 .0060 .0080 .0104 .0136 .0174 .0222 .0281 .0351 .0436 .0537 .0655 .0793 .0951 .1131 .1335 .1562 .1814 .2090 .2389 .2709 .3050 .3409 .3783 .4168 .4562 .4960 .0003 .0005 .0006 .0009 .0013 .0018 .0024 .0033 .0044 .0059 .0078 .0102 .0132 .0170 .0217 .0274 .0344 .0427 .0526 .0643 .0778 .0934 .1112 .1314 .1539 .1788 .2061 .2358 .2676 .3015 .3372 .3745 .4129 .4522 .4920 .0003 .0004 .0006 .0009 .0012 .0017 .0023 .0032 .0043 .0057 .0075 .0099 .0129 .0166 .0212 .0268 .0336 .0418 .0516 .0630 .0764 .0918 .1093 .1292 .1515 .1762 .2033 .2327 .2643 .2981 .3336 .3707 .4090 .4483 .4880 .0003 .0004 .0006 .0008 .0012 .0016 .0023 .0031 .0041 .0055 .0073 .0096 .0125 .0162 .0207 .0262 .0329 .0409 .0505 .0618 .0749 .0901 .1075 .1271 .1492 .1736 .2005 .2296 .2611 .2946 .3300 .3669 .4052 .4443 .4840 .0003 .0004 .0006 .0008 .0011 .0016 .0022 .0030 .0040 .0054 .0071 .0094 .0122 .0158 .0202 .0256 .0322 .0401 .0495 .0606 .0735 .0885 .1056 .1251 .1469 .1711 .1977 .2266 .2578 .2912 .3264 .3632 .4013 .4404 .4801 .0003 .0004 .0006 .0008 .0011 .0015 .0021 .0029 .0039 .0052 .0069 .0091 .0119 .0154 .0197 .0250 .0314 .0392 .0485 .0594 .0721 .0869 .1038 .1230 .1446 .1685 .1949 .2236 .2546 .2877 .3228 .3594 .3974 .4364 .4761 .0003 .0004 .0005 .0008 .0011 .0015 .0021 .0028 .0038 .0051 .0068 .0089 .0116 .0150 .0192 .0244 .0307 .0384 .0475 .0582 .0708 .0853 .1020 .1210 .1423 .1660 .1922 .2206 .2514 .2843 .3192 .3557 .3936 .4325 .4721 .0003 .0004 .0005 .0007 .0010 .0014 .0020 .0027 .0037 .0049 .0066 .0087 .0113 .0146 .0188 .0239 .0301 .0375 .0465 .0571 .0694 .0838 .1003 .1190 .1401 .1635 .1894 .2177 .2483 .2810 .3156 .3520 .3897 .4286 .4681 .0002 .0003 .0005 .0007 .0010 .0014 .0019 .0026 .0036 .0048 .0064 .0084 .0110 .0143 .0183 .0233 .0294 .0367 .0455 .0559 .0681 .0823 .0985 .1170 .1379 .1611 .1867 .2148 .2451 .2776 .3121 .3483 .3859 .4247 .4641 Final, Business Statistics I 7 Standard Normal Probabilities Table entry Table entry for z is the area under the standard normal curve to the left of z. z z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .5000 .5398 .5793 .6179 .6554 .6915 .7257 .7580 .7881 .8159 .8413 .8643 .8849 .9032 .9192 .9332 .9452 .9554 .9641 .9713 .9772 .9821 .9861 .9893 .9918 .9938 .9953 .9965 .9974 .9981 .9987 .9990 .9993 .9995 .9997 .5040 .5438 .5832 .6217 .6591 .6950 .7291 .7611 .7910 .8186 .8438 .8665 .8869 .9049 .9207 .9345 .9463 .9564 .9649 .9719 .9778 .9826 .9864 .9896 .9920 .9940 .9955 .9966 .9975 .9982 .9987 .9991 .9993 .9995 .9997 .5080 .5478 .5871 .6255 .6628 .6985 .7324 .7642 .7939 .8212 .8461 .8686 .8888 .9066 .9222 .9357 .9474 .9573 .9656 .9726 .9783 .9830 .9868 .9898 .9922 .9941 .9956 .9967 .9976 .9982 .9987 .9991 .9994 .9995 .9997 .5120 .5517 .5910 .6293 .6664 .7019 .7357 .7673 .7967 .8238 .8485 .8708 .8907 .9082 .9236 .9370 .9484 .9582 .9664 .9732 .9788 .9834 .9871 .9901 .9925 .9943 .9957 .9968 .9977 .9983 .9988 .9991 .9994 .9996 .9997 .5160 .5557 .5948 .6331 .6700 .7054 .7389 .7704 .7995 .8264 .8508 .8729 .8925 .9099 .9251 .9382 .9495 .9591 .9671 .9738 .9793 .9838 .9875 .9904 .9927 .9945 .9959 .9969 .9977 .9984 .9988 .9992 .9994 .9996 .9997 .5199 .5596 .5987 .6368 .6736 .7088 .7422 .7734 .8023 .8289 .8531 .8749 .8944 .9115 .9265 .9394 .9505 .9599 .9678 .9744 .9798 .9842 .9878 .9906 .9929 .9946 .9960 .9970 .9978 .9984 .9989 .9992 .9994 .9996 .9997 .5239 .5636 .6026 .6406 .6772 .7123 .7454 .7764 .8051 .8315 .8554 .8770 .8962 .9131 .9279 .9406 .9515 .9608 .9686 .9750 .9803 .9846 .9881 .9909 .9931 .9948 .9961 .9971 .9979 .9985 .9989 .9992 .9994 .9996 .9997 .5279 .5675 .6064 .6443 .6808 .7157 .7486 .7794 .8078 .8340 .8577 .8790 .8980 .9147 .9292 .9418 .9525 .9616 .9693 .9756 .9808 .9850 .9884 .9911 .9932 .9949 .9962 .9972 .9979 .9985 .9989 .9992 .9995 .9996 .9997 .5319 .5714 .6103 .6480 .6844 .7190 .7517 .7823 .8106 .8365 .8599 .8810 .8997 .9162 .9306 .9429 .9535 .9625 .9699 .9761 .9812 .9854 .9887 .9913 .9934 .9951 .9963 .9973 .9980 .9986 .9990 .9993 .9995 .9996 .9997 .5359 .5753 .6141 .6517 .6879 .7224 .7549 .7852 .8133 .8389 .8621 .8830 .9015 .9177 .9319 .9441 .9545 .9633 .9706 .9767 .9817 .9857 .9890 .9916 .9936 .9952 .9964 .9974 .9981 .9986 .9990 .9993 .9995 .9997 .9998 Final, Business Statistics I 8