805-2000-test

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| Statistics Topic Test Braddock Invitational — February 26, 2000 Note: For each of the followifig questions, answer E, NOTA, means "None of the Above." 1. The grade point averages (GPA) of 7 randomly chosen students from your statistics class are 314 237 294 360 170 400 1.8S If > (x—¥)* =4.51, then the standard deviation is A. 075 B. 0.87 C. 064 D. .80 E.NOTA 2. The scores on a statistics exam are strongly skewed to the left. So it is best to describe the distribution by reporting . A. the five-number summary B. the mean and the standard deviation C. the mean, the median, and the mode D. the correlation and its square E. NOTA 3. A standardized test designbd to measure math anxiety has a mean of 100 and a standard deviation of 10 in the population of first year college students. Which of the following observations would you expect is an outlier? A. 150 B. 120 C. 90 D. all ofthe above E. NOTA 4. The central limit theorem §tates that the sample mean is unbiased the sample mean is approximately normal the binomial distribution is skewed the sample standard deviation is approximately normal NOTA | moawy 5. You want to compute a 95% confidence interval for the population mean. Assume that the population standard deviation is known to be 10 and the sample size is 50. The value of z* to be used in this calculation is A 1.645 B. 2.009 C. 8239 D. 8352 E. NOTA

10. Statistics Topic Test Braddock Invitational — February 26, 2000 A significance test was performed to test the null hypothesis Ho: p = 2 versus the alternative Ha: pt #2. The test statistic is z = 1.40. The p-value for this test is approximately A. 0.08 B. 0.92 C. 0.16 D. 0.84 E. NOTA A 95% confidence interval for the mean reading achievement score for a population of third grade students is (44.2, 54.2). Suppose you compute a 99% confidence interval. Which of the following statements is correct? A. the intervals have the same width B. the 99% interval is wider C. the 95% interval is wider D. you cannot determine which interval is wider unless you know n and s E. NOTA A two-way table of counts is analyzed to examine the hypothesis that the row and column classifications are independent. There are 3 rows and 4 columns. The degrees of freedom for the 7 statistic are A 12 B. 6 C n-1 D. the minimumofn, -1 andn, ~ 1 E. NOTA You want to compute a 90% confidence interval for the mean of a population with unknown population standard deviation. The sample size is 30. The value of t” you would use for this interval is A 196 B. 1.645 C. 1.699 D. 0.90 E. NOTA A randomly selected student is asked to respond yes, no, or maybe to the question: "Do you intend to vote in the next presidential election?" The sample space is {yes, no, maybe}. Which of the following represent a legitimate assignment of probabilities for this sample space? A 04,04,02 B. 04,0604 C 03,03,03 D 0503-02 E NOTA

11 12. 13. 14. Statistics Topic Test Braddock Invitational — February 26, 2000 You play tennis regularly with a friend and from past experience you believe that the outcome of each match is independent. For any given match you have a probability of 0.6 of winning. The probability that you win the next two matches is A. 036 B. 0.6 C.04 D. 0.16 E. NOTA If you play tennis with your friend in problem 11 five times, what is the probability that you win exactly two of those matches? A 36 B. .02304 C. 2304 D. 31744 E. NOTA A sample survey chooses a sample of households and measures their annual income and their savings. Some events of interest are: A = the household chosen has income at least $50,000 C = the household chosen has at least $10,000 in savings Based on the sample survey, we estimate that P(A) = 0.2 and P(C) = 0.3. The probability that a household has income at least $50,000 or savings at least $10,000 | is 0.5 is 0.06 can't be found from this information because A and C are probably not disjoint can't be found from this information because A and C are probably not independent NOTA mooOw> In a study of the effects of acid rain, a random sample of 100 trees from a particular forest are examined. Forty percent of these show some signs of damage. Which of the following statements is correct? The sampling distribution of the proportion of damaged trees is approximately normal. If we took another random sample of trees, we would find that 40% of these would show some signs of damage. If a sample of 1000 trees was examined the variability of the sample proportion would be larger than for a sample of 100 trees. This is a comparative experiment. NOTA mo O wp

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15. 16. 17. 18. 19. Statistics Topic Test Braddock Invitational — February 26, 2000 A student organization wants to assess the attitudes of students toward a proposed change in the hours that the library is open. They randomly select 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors. The situation described is A. a stratified random sample B. a simple random sample C. a comparative experiment D. anecdotal evidence E. NOTA In a statistics course a linear regression equation was computed to predict the final exam score on the first test. The equation was y =10+ 0.9x where y is the final exam score and x 15 the score on the first exam. Eve scored 95 on the first test. On the final exam Eve scored 98. What is the value of her residual? A. 98 B. 25 C. -25 D. 0 E. NOTA The reversal of the direction of an association when lurking variables are taken into account is called A. Simpson's Paradox B. negative association C. least-squares regression D. aresidual plot E. NOTA Do women and men treat female and male children differently? An observational study was conducted near the primate exhibit at the Sacramento Zoo on weekends in 1988. The data are from 39 groups of three (one adult female, one adult male, and one toddler) in which the toddler was being carried. ' Recorded below are which adult (male or female) was carrying the toddler by the sex of the toddler Sex of the toddler Male Female Sex of adult carrying toddier Male 8 17 Female 6 8 The numerical value of the chi-square statistic for testing independence of sex of the adult and sex of the toddler is A. 0.460 B. 0.498 C.3.84 - D. 39.27 E. NOTA Which of the following is not a major principle of experimental design? A. comparative experimentation B. replication C. randomization D. segmentation E. NOTA

20. 21. 22. 23. Statistics Topic Test Braddock Invitational — February 26, 2000 The probability density of a random variable X is given in the figure below. T 0 | 2 X The probability that X is at least 1.5 is A 0 B. 1/4 C. 173 D 1/2 E. NOTA A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution X 0o 1 2 3 4 P(X) 0.1 0.1 01 0.1 0.6 The standard deviation of the number of customers that make a purchase during the first hour that the store is open is A 40 B 30 C. 20 D 14 E. NOTA Suppose A is a random variable with mean 1, and standard deviation c,. Suppose Y is a random variable with mean uy and standard deviation 6y. The mean of X + Y is A pxt py B (uv/ox) + (/oY) C. px+ uy, but onlyif A and Y are independent D. (py/ox) + (Ux/oy), but only if X and Y are independent E. NOTA A sociologist is studying the effect of having children within the first two years of marriage on the divorce rate. Using hospital birth records, she selects a random sample of 200 couples who had a child within the first two years of marriage. Following up on these couples, she finds that 80 couples are divorce within 5 years. A 90% confidence interval for the proportion of couples who had a child within the first two years of marriage and are divorced within five years is A. 040 £ 0035 B. 040+0.044 C. 0.40+0.057 D. 040+0.068 E. NOTA

24. 25. 26. 27. Statistics Topic Test Braddock Invitational — February 26, 2000 An SRS of size 100 is taken from a population having proportion 0.8 of successes. An independent SRS of size 400 is taken from a population having proportion 0.5 of successes. The sampling distribution for the difference in the sample proportions, p, — p,, has standard dewviation equal to A 13 B. 0.40 C. 0.047 D. 0.002 E. NOTA Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of $2, and the amount spent has a normal distribution with a standard deviation 6 = $30. The number of observations required is closest to A 25 B. 30 C. 609 D. 865 E. NOTA An SRS of size 15 is drawn from a population that has a normal distribution with mean p and standard deviation s. The one-sample t statistic, % has how many degrees of s freedom? A. 15 B. 14 c V5 D. cannot be determined E. NOTA For the density curve below, which of the following is true? A The mean 2nd median are equal. B. The mean 1s greater than the median. C. The mean is less than the median. D. The mean could be either greater than or less than the median. E. NOTA

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28. 29. 30. Statistics Topic Test Braddock Invitational — February 26, 2000 The weights of packets of cookies produced by a certain manufacturer have a normal distribution with a mean of 202g and a standard deviation of 3g. The weight that should be stamped on the packet so that only 1% of packets are underweight is A. 209g B. 195g C. 202g D. cannot be determined E. NOTA Parts manufactured by an injection molding process are subjected to a compressive strength test. We wish to monitor the compressive strength of the parts manufactured by this process using an X control chart. Samples of size nine are to be taken at regular intervals and their mean compressive strength (in psi = pounds per square inch) is plotted on the chart in time order. The target values for the compressive strengths are a mean of |1 = 80 psi and a standard deviation of ¢ = 3 psi. Suppose at the time of sample 10, a mean of 85 psi is observed. One should declare the process out-of-control. continue sampling. The process is still in-control. continue sampling, but increase the sample size to 16. The process is barely in-control. . continue sampling, but reduce the sample size to 4. The process is well in-control. NOTA Mo Ow e Other things being equal, the margin of error of a confidence interval increases as the sample size increases. the confidence level decreases. the population standard deviation increases. all of the above. NOTA moows

Probability Probability Table entry Table entry for z is the for z is the probability probability lying below z. lying below z. | Z Table A (Continued) Table A Standard normal probabilities g 90 . — 03 o % 8 97 08__ B . : 00 | 5000 5040 5080 5120 5160 5199 5239 5279 5319 5359 .00 01 02 03 04 05 08 07 N = - : . . 08 09 o1 | 5398 5438 5478 5517 5557 5596 5636 5675 5714 5753 A 3882 0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002 0.2 5793 5832 5871 5910 5948 5987 .6026 6064 6103 .6141 23 00Ds 0005 0005 0004 0004 0004 .0004 0004 0004 0003 03 | 6179 6217 6255 6293 6331 .6368 6406 6443 6480 6517 Sz a0 .gggg .8006 0006 0006 .0006 0005 0006 .0005 04 | 6554 6591 6628 6664 6700 6736 6772 6808 6841 6879 1000 0009 0009 .0809 0008 0008 .0008 .0008 .0007 .0007 05 | 6915 6950 6985 7019 7054 7088 7123 7157 7190 7224 -3 0013 00180018 0012 gglg 0011 0011 0011 .0010 .0010 06 | 7257 7201 7324 7357 71389 7422 1454 7486 7517 .T549 YR ey S O3 .%g 0015 0015 .0014 .0014 07 | 7580 7611 642 7673 704 .T734 7764 7794 7823 78G2 E R o021 0ozl Doz 0019 08 | 7881 7910 7939 7967 7995 8023 8051 8078 8106 .BL3 56 0047 0045 0044 0043 0041 0040 0039 -gggg 0027 0026 00 | 8159 8186 8212 8238 .8264 8280 8315 .8340 8365 .B3% 52 0062 0060 0059 0057 0055 0054 | : 0037 0036 10 | ‘8413 8438 8461 8485 8508 8531 8554 8577 8509 .86l SR - L o B S e S 1 | 8643 8665 8686 8708 8729 8749 8770 8790 8810 8830 L0107 0104 0102 0099 009G 0094 0001 . : : 12 | ‘as49 8869 8888 8907 8925 8944 8962 8980 8997 9015 2 0139 013 0132 0120 0125 0122 0119 o6 03 0110 13 | 02 9049 9066 9082 9099 SU5 9181 9T HEE T DGR MR O R BR N 02 % O aF S 5 R SRR 19 0287 0281 0274 0268 0262 0256 0250 0244 0239 .0233 16 | 0452 0463 9474 9484 9495 9505 9515 9525 9585 904D -1.8 - 0359 0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294 1.7 9554 9564 9573 .9582 9591 .9599 9608 9616 .96256 .9633 (75 0446 0436 0427 0418 .0409 .0401 0392 .0384 0375 .0367 18 | ‘9641 9649 9656 9664 9671 9678 9686 9693 9699 9706 g 0548 0537 0526 0516 0505 0495 .0485 0475 0465 .0455 L9 | 9713 o1 9726 9732 9738 9744 9750 9756 9761 9707 5 0668 0685 0643 0630 0618 0606 0594 .0582 0571 .0559 o0 | o772 9778 9783 9788 9793 9798 9803 9808 9812 .9817 L sis 083 078 0764 0749 0785 0721 0708 0694 0681 51 | ‘o821 9826 9330 9834 9838 9842 9846 9850 9854 98T oo 0351 (llslafé 0918 0901 0885 0869 0853 088 0823 o0 | o361 0864 0868 9871 9875 9878 9881 .9BB4 9887 980 2 b8z 008 1075 1056 1038 1020 1003 0985 53 | 9893 9896 9898 9901 9904 9906 9909 9911 9913 9916 R A S+ (4 1251 ifig 1210 1190 .1170 54 | 9918 0920 9922 9925 9927 9920 9931 9932 9934 9936 e s iy loes 1423 1401 1379 o5 | ‘9938 9940 9941 9943 9945 9946 9948 9949 9951 9952 oS 2119 2090 2061 2033 2005 1977 1949 1922 1685 181 o6 | 9953 9955 9956 9957 9959 9960 9961 9962 9963 9964 e s sose bes 211 D o7 | 9965 9966 9967 9968 9969 9970 9971 9972 9973 9974 06 27143 2709 2676 2 ' prty B 21 o8 | 9974 9975 9976 9977 9977 9978 9979 9979 9980 .99l T e B+ S S s 2483 2451 5o | 9981 9982 982 0983 9984 9984 9985 9985 9986 998G U, - . . . 294 . 912 2877 . . . . . o~ , . . . . . . . 04 3446 3400 3372 3336 3300 264 3228 e A 50 | ‘9957 0987 9987 9988 9988 9989 9989 9980 .9990 9990 -03 3521 3783 3745 3707 3669 . 3632 3594 3557 3520 3483 a1 | 9990 9991 9991 0991 9992 9992 9992 9992 9993 993 02 4207 4168 4129 4090 4052 4013 3974 3936 3897 3859 52 | 9093 9993 0994 9994 9994 9994 9994 9995 9995 UYUS W1 4602 4562 4522 4483 4443 4404 4364 4325 4286 4247 53 | 9995 (9995 9995 9996 9996 9996 9996 9996 9996 9997 00 5000 4960 4920 4880 4840 4801 4761 4721 4681 = 4641 34 | 9997 9997 9997 9997 9997 9997 9997 INVT 9997 9998 i 16

Table entry for p and C is the point t* with probabil- ity p lying above Probability p Table entry it and probability for p is the Probability p C lying between point (X?) with -t* and t*. probability p ¥ lying above it. : L " (X% Table B t distribution critical values 2 ] Tail probability p Table C X criticgl valugs_ df 725 20 15 10 .05 025 .02 01 _.005 .0025 001 .0005 . . Mailprobabilityp L 1 |1.000 1376 1.963 3.078 6314 1271 1589 3182 63.66 127.3 3183 6366 i 25 20 15 10 05 025 02 .01 005 0025 001 2 | 816 1.061 1.386 1.886 2920 4.303 4.849 6.965 9.925 14.09 22.33 31.60 1 132 164 207 271 38 502 541 663 788 914 10.83 3 | 765 978 1.250 1.638 2.353 3.182 3.482 4.541 5841 7453 1021 12.92 2 277 322 379 461 599 738 782 921 1060 1198 13.82 4 73% 941 1.190 1533 2.132 2.776 2323 g.gm 4.60;_ 5598 17.173 8.618 3 411 464 532 625 781 935 984 1134 1284 1432 1627 5 | 727 920 1156 1476 2015 2571 2. 365 4.032 4.773 5.893 6.86 4 539 593 674 778 949 1114 1167 1328 1486 1642 1847 7 | 711 8% 1.119 1:415 1:895 2.365 2517 2.998 3499 4.029 4.785 5.408 6 781 856 945 1064 1259 1445 1503 1681 1855 2025 2246 8 | 706 .889 1.108 1.397 1:860 2306 2.449 2.896 3.355 3.833 4.501 5.041 y - : - y : g - : : : 9 | .703 883 1.100 1.383 1.833 2262 2398 2821 3250 3.690 4.297 4.781 7 904 980 1075 1202 1407 1601 1662 1848 20.28 22.04 24.32 10 700 879 1.093 1372 1812 2228 2359 2764 3.169 3581 4.144 4.587 8 1022 11.03 1203 1336 1551 17.53 1817 20.09 2195 2397 26.12 11 | 697 .876 1.088 1.363 1.796 2201 2328 2.718 3.106 3.497 4.025 4.437 9 1139 1224 1329 1468 1692 19.02 1968 21.67 2359 2546 27.65 12 | 695 .873 1.083 1.356 1.782 2179 2.303 2.681 3.055 3.428 3.930 4.318 10 1255 1344 1453 1599 1831 2048 21.16 2321 2519 27.11 435 is ggg .ggg lggg 1.350 1.%1 g.mo 2.23 gggo gg%?.{ gggg 3.332 4.22(1) 11 1370 1463 1577 1728 1968 2192 2262 2472 26.76 2873 31.9% 4 1. 868 1.076 1345 1.761 2.145 2.264 2.624 2. . 187 4.14 12 14.85 1581 1699 1855 21.03 2334 24.05 2622 2830 3032 3241 15 691 866 1.074 1.341 1.753 2.131 2.249 2.602 2.947 3.286 3.733 4.073 13 1598 1698 1820 19.81 2236 24.74 2547 2169 2982 31.88 34‘1:_.__-1), 17 | 689 .863 1.069 1.333 1.740 2:110 2224 2567 2.898 3.222 3.646 8.965 15 1825 1931 2060 2231 2500 2749 2826 5058 3280 3195 5770 18 | 688 .862 1.067 1.330 1.734 2101 2214 2552 2.878 3.197 3.611 3.922 - : : : . : - . - . : 19 | 688 .861 L.066 1.328 1.729 2.093 2205 2539 2.861 3.174 3.579 3.883 16 1937 2047 21.79 2354 2630 2885 2963 3200 3427 36.46 39.25 20 | 687 860 1.064 1.325 1.725 2086 2197 2528 2.845 3.153 3.552 3.850 17 2049 2161 2298 24.77 2759 30.19 31.00 3341 3572 37.95 40.79 21 | 686 .859 1.063 1.323 1.721 2.080 2.189 2518 2.831 3.135 3.527 3.819 18 2160 2276 24.16 2599 2887 3153 3235 34.81 37.16 3942 4231 22 | 686 .858 1.061 1321 1.717 2.074 2.183 2508 2.819 3.119 3.505 3.792 19 2272 2390 2533 2720 30.14 3285 33.69 3619 3858 40.88 43.82 23 .egs 858 1.860 1.313 1.714 2069 2.177 2.500 gggg( g.(l)gfx 3.425 3.76§ 20 2383 2504 2650 2841 3141 34.17 3502 3757 40.00 4234 4531 24 | 685 .857 1.059 1318 1.711 2.064 2172 2492 2. 091 3467 3.74 9403 9 ‘62 2967 354 . 78 468 25 | 684 .856 1.058 1.316 1.708 2.060 2.167 2.485 2.787 3.078 3.450 3.725 §; 26 84 2?,;(7, gggg §g g‘f 3§ gz 36 73 gggé 3333 2 gg ig ;fi 48'29, 26 | 684 856 1.058. 1.315 1.706 2.056 2.162 2479 2.779 3.067 3.435 3.707 y : - ' . ' : - . i ", 23 27.4 2843 2998 3201 3517 38.08 3897 4164 44.18 4662 4973 27 | 684 .855 1.057 1.314 1.703 2052 2.158 2473 2771 3.057 3.421 3.690 ; ‘ .1 28 | 683 855 1.056 1.313 1.701 2.048 2154 2467 2.763 3.047 3.408 3.674 24 2824 2955 3113 3320 3642 3936 4027 4298 4556 4803 5118 29 683 854 1.055 1.311 1.699 2.045 2.150 2462 2.756 3.038 3.396 3.659 256 29.34 30.68 32.28 3438 37.65 40.65 4157 4431 4693 4944 5262 30 | 683 .854 1.055 1.310 1.697 2.042 2.147 2457 2.750 3.030 3.385 3.646 26 3043 31.79 3343 3556 38.89 41.92 4286 4564 4829 50.83 54.05 40 | 681 .851 1.050 1.303 1.684 2021 2.123 2423 2.704 2.971 3.307 3.55 27 3153 3291 3457 3674 40.11 43.19 44.14 4696 4964 5222 5548 50 | 679 849 1.047 1.532 1.2;16 g.oog 2109 2.403 2.678 2.93;1 ggg‘lz 3.496 28 3262 3403 3571 3792 41.34 4446 4542 4828 5099 5359 56.89 60 | 673 848 1.045 1.296 1.671 2.000 2.099 2.390 2.660 2.915 3.232 3.4G0 29 3371 35.14 3685 39.09 4256 4572 46.69 4959 5234 5497 5830 80 | 678 846 1043 1292 1664 1990 2088 2374 2639 2887 3.195 341G 30 3480 3625 37.99 4026 4377 4698 4796 5089 5367 5633 59.70 oy | 7T 845 1042 1290 1660 1984 2081 2.364 posy Iy SATA 3550 40 4562 4727 4924 5181 5576 59.31 60.44 6369 66.77 69.70 73.40 | s e e s 1 i s B0 2 U5 U Dofm s mE miue 0w mu ok nw sw o0% 60% Wk 0% % 9% X% 8% 9% 095% 998% 90.9% 8 8813 9041 9311 9658 1019 1066 1081 1123 1163 1201 1248 100 109.1 1117 1147 1185 1243 1296 1311 1358 1402 1443 1494 18

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