ap真題2018ap18frq statistics

1、2018AP Statistics-Response Questions© 2018 The Colleg. Colleg, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the Colleg. Visit the Colleg on the Web: .AP Central is the official online home for the AP Program: .2018 AP® STAT

2、ISTICS -RESPONSE QUESTIONSFormulas begin on page 3. Questions begin on page 6. Tables begin on page 12.-2-2018 AP® STATISTICS FREE-RESPONSE QUESTIONSFormulas(I) Descriptive StatisticsxÇ xi n 1 n 1Ç x xi 2sx n 1 s n1 212 1 s 22 n1 1 n2 1 spy b0 b1xÇ xi x yi y -5-2b1 Ç xi x b0

3、 y b1xr 1 ÇÈ xi x Ø È yi y ØÚsn 1ÉÊsxÙ ÉÙÊyÚb r sy1sxÇ y y 2i1 i i s n 2 bÇ x x 2(II) ProbabilityP(A ª B) P(A) P(B) P( A © B)P( A B) P( A © B)P(B)E(X ) m x Ç xi piVar(X ) s 2 Ç x m 2 pxixiIf X has a b

4、inomial distribution with parameters n and p , then:É ÙP(X k) È nØ pk (1 p)n kÊ kÚm x npnp(1 p)sxm p p p(1 p)ns p If x is the mean of a random sample of size n from an infinite population with mean m and standard deviation s, then:m x mnsxs(III) Inferential StatisticsSt

5、andardized test statistic:statistic parameterstandard deviation of statisticConfidence interval: statistic critical value standard deviation of statistic Single-SampleStatisticStandard Deviation of StatisticSample MeansnSample Proportion p(1 p)nof StatisticTwo-SampleStatisticStandard DeviationDiffer

6、ence of sample means s 2 s 212 n1n2Special case when s1 s2s 1 1 n1n2Difference of sample proportionsp1(1 p1 ) p2 (1 p2 )n1n2Special case when p1 p2p 1 p1 1 n1n2Chi-square test statistic Ç observed expected 2 expected2018 AP® STATISTICS-RESPONSE QUESTIONSSTATISTICS SECTION IIPart A Question

7、s 1-5Spend about 1 hour and 5 minutes on this part of the exam.Percent of Section II score 75Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanation

8、s.1. The manager of a grocery store selected a random sample of 11 customers to investigate the relationship between the number of customers in a checkout line and the time to finish checkout. As soon as the selected customer entered the end of a checkout line, data were collected on the number of c

9、ustomers in line who were in front of the selected customer and the time, in seconds, until the selected customer was finished with the checkout. The data are shown in the following scatterplot along with the corresponding least-squares regression line and computer output.PredictorCoefSE CoefTPConst

10、ant72.95110.360.660.525Customers in line174.4035.064.970.001S = 200.01R-Sq = 73.33%R-Sq (adj) = 70.37%(a) Identify and interpret in context the estimate of the intercept for the least-squares regression line.(b) Identify and interpret in context the coefficient of determination, r 2 .(c) One of the

11、data points was determined to be an outlier. Circle the point on the scatterplot and explain why the point is considered an outlier.© 2018 The Collegon the Web:.Visit the Colleg.GO ON TO THE NEXT PAGE.-10-2. An environmental science teacher at a high school with a large population of s wanted t

12、o estimate the proportion of s at the school who regularly recycle plastic bottles. The teacher selected a random sample of s at the school to survey. Each selected went into the teachers office, one at a time, and was asked to respond yes or no to the following question.Do you regularly recycle pla

13、stic bottles?Based on the responses, a 95 percent confidence interval for the proportion of all s at the school who would respond yes to the question was calculated as (0.584, 0.816).(a) How many s were in the sample selected by the environmental science teacher?(b) Given the method used by the envi

14、ronmental science teacher to collect the responses, explain how bias might have been introduced and describe how the bias might affect the point estimate of the proportion of all s at the school who would respond yes to the question.(c) The statistics teacher at the high school was concerned about t

15、he potential bias in the survey. To obtain a potentially less biased estimate of the proportion, the statistics teacher used an alternate method for collecting responses. A random sample of 300 s was selected, and each was given the following instructions on how to respond to the question. In privat

16、e, flip a fair coin. If heads, you must respond no, regardless of whether you regularly recycle. If tails, please tfully respond yes or no.(i) What is the expected number of s from the sample of 300 who would be required to respond no because the coin flip resulted in heads?(ii) The results of the s

17、ample showed that 213 of the 300 selecteds responded no. Based on the results of the sample, give a point estimate for the proportion of alls at the high school who would respond yes to the question.3. Approximately 3.5 percent of all children born in a certain region are from multiple births (that

18、is, twins, triplets, etc.). Of the children born in the region who are from multiple births, 22 percent are left-handed. Of the children born in the region who are from single births, 11 percent are left-handed.(a) What is the probability that a randomly selected child born in the region is left-han

19、ded?(b) What is the probability that a randomly selected child born in the region is a child from a multiple birth, given that the child selected is left-handed?(c) A random sample of 20 children born in the region will be selected. What is the probability that the sample will have at least 3 childr

20、en who are left-handed?4. The anterior cruciate ligament (ACL) is one of the ligaments that help stabilize the knee. Surgery is often recommended if the ACL is completely torn, and recovery time from the surgery can be lengthy. A medical center developed a new surgical procedure designed to reduce t

21、he average recovery time from the surgery. To test the effectiveness of the new procedure, a study was conducted in which 210 patients needing surgery to repair a torn ACL were randomly assigned to receive either the standard procedure or the new procedure.(a) Based on the design of the study, would

22、 a statistically significant result allow the medical center to conclude that the new procedure causes a reduction in recovery time compared to the standard procedure, for patients similar to those in the study? Explain your answer.(b) Summary statistics on the recovery times from the surgery are sh

23、own in the table.Type of ProcedureSampleSizeMean Recovery Time (days)Standard Deviation Recovery Time (days)Standard11021734New10018629Do the data provide convincing statistical evidence that those who receive the new procedure will have less recovery time from the surgery, oage, than those who rece

24、ive the standard procedure, for patients similar to those in the study?5. The following histograms summarize the teaching year for the teachers at two high schools, A and B.Teaching year is recorded as an integer, with first-year teachers recorded as 1, second-year teachers recorded as 2, and so on.

25、 Both sets of data have a mean teaching year of 8.2, with data recorded from 200 teachers at High School A and 221 teachers at High School B. On the histograms, each interval represents possible integer values from the left up to but not including the right .(a) The median teaching year for one high

26、 school is 6, and the median teaching year for the other high school is7. Identify which high school has each median and justify your answer.(b) An additional 18 teachers were not included with the data recorded from the 200 teachers at High School A. The mean teaching year of the 18 teachers is 2.5

27、. What is the mean teaching year for all 218 teachers at High School A?(c) The standard deviation of the teaching year for the 221 teachers at High School B is 7.2. If one teacher is selected at random from High School B, what is the probability that the teaching year for the selected teacher will b

28、e within 1 standard deviation of the mean of 8.2 ? Justify your answer.2018 AP® STATISTICS-RESPONSE QUESTIONSSTATISTICS SECTION IIPart B Question 6Spend about 25 minutes on this part of the exam.Percent of Section II score 25Directions: Show all your work. Indicate clearly the methods you use,

29、because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.6. Systolic blood pressure is the amount of pressure that blood exerts on blood vessels while the heart is beating. The mean systolic blood pressure for people i

30、n the United States is reported to be 122 millimeters of mercury (mmHg) with a standard deviation of 15 mmHg.The wellness department of a large corporation is investigating whether the mean systolic blood pressure of its employees is greater than the reported national mean. A random sample of 100 em

31、ployees will be selected, the systolic blood pressure of each employee in the sample will be measured, and the sample mean will be calculated.Let m represent the mean systolic blood pressure of all employees at the corporation. Consider the following hypotheses.H0 : m = 122 Ha : m > 122(a) Descri

32、be a Type II error in the context of the hypothesis test.(b) Assume that s, the standard deviation of the systolic blood pressure of all employees at the corporation, is 15 mmHg. If m = 122, the sampling distribution of x for samples of size 100 is approximately normal with a mean of 122 mmHg and a

33、standard deviation of 1.5 mmHg. What values of the sample mean x would represent sufficient evidence to reject the null hypothesis at the significance level of a = 0.05 ?The actual mean systolic blood pressure of all employees at the corporation is 125 mmHg, not the hypothesized value of 122 mmHg, a

34、nd the standard deviation is 15 mmHg.(c) Using the actual mean of 125 mmHg and the results from part (b), determine the probability that the null hypothesis will be rejected.(d) What statistical term is used for the probability found in part (c) ?(e) Suppose the size of the sample of employees to be

35、 selected is greater than 100. Would the probability of rejecting the null hypothesis be greater than, less than, or equal to the probability calculated in part (c) ? Explain your reasoning.STOP END OF EXAM© 2018 The Colleg.Visit the Colleg on the Web:.-11-2018 AP® STATISTICS FREE-RESPONSE

36、 QUESTIONSzProbabilityTable entry for z is the probability lying below z.Table A Standard normal probabilitiesz.00.01.02.03.04.05.06.07.08.09 3.4.0003.0003.0003.0003.0003.0003.0003.0003.0003.0002 3.3.0005.0005.0005.0004.0004.0004.0004.0004.0004.0003 3.2.0007.0007.0006.0006.0006.0006.0006.0005.0005.0

37、005 3.1.0010.0009.0009.0009.0008.0008.0008.0008.0007.0007 3.0.0013.0013.0013.0012.0012.0011.0011.0011.0010.0010 2.9.0019.0018.0018.0017.0016.0016.0015.0015.0014.0014 2.8.0026.0025.0024.0023.0023.0022.0021.0021.0020.0019 2.7.0035.0034.0033.0032.0031.0030.0029.0028.0027.0026 2.6.0047.0045.0044.0043.00

38、41.0040.0039.0038.0037.0036 2.5.0062.0060.0059.0057.0055.0054.0052.0051.0049.0048 2.4.0082.0080.0078.0075.0073.0071.0069.0068.0066.0064 2.3.0107.0104.0102.0099.0096.0094.0091.0089.0087.0084 2.2.0139.0136.0132.0129.0125.0122.0119.0116.0113.0110 2.1.0179.0174.0170.0166.0162.0158.0154.0150.0146.0143 2.

39、0.0228.0222.0217.0212.0207.0202.0197.0192.0188.0183 1.9.0287.0281.0274.0268.0262.0256.0250.0244.0239.0233 1.8.0359.0351.0344.0336.0329.0322.0314.0307.0301.0294 1.7.0446.0436.0427.0418.0409.0401.0392.0384.0375.0367 1.6.0548.0537.0526.0516.0505.0495.0485.0475.0465.0455 1.5.0668.0655.0643.0630.0618.060

40、6.0594.0582.0571.0559 1.4.0808.0793.0778.0764.0749.0735.0721.0708.0694.0681 1.3.0968.0951.0934.0918.0901.0885.0869.0853.0838.0823 1.2.1151.1131.1112.1093.1075.1056.1038.1020.1003.0985 1.1.1357.1335.1314.1292.1271.1251.1230.1210.1190.1170 1.0.1587.1562.1539.1515.1492.1469.1446.1423.1401.1379 0.9.1841

41、.1814.1788.1762.1736.1711.1685.1660.1635.1611 0.8.2119.2090.2061.2033.2005.1977.1949.1922.1894.1867 0.7.2420.2389.2358.2327.2296.2266.2236.2206.2177.2148 0.6.2743.2709.2676.2643.2611.2578.2546.2514.2483.2451 0.5.3085.3050.3015.2981.2946.2912.2877.2843.2810.2776 0.4.3446.3409.3372.3336.3300.3264.3228

42、.3192.3156.3121 0.3.3821.3783.3745.3707.3669.3632.3594.3557.3520.3483 0.2.4207.4168.4129.4090.4052.4013.3974.3936.3897.3859 0.1.4602.4562.4522.4483.4443.4404.4364.4325.4286.4247 0.0.5000.4960.4920.4880.4840.4801.4761.4721.4681.4641-13-ProbabilityTable entry for z is the probability lying below z.zTa

43、ble A (Continued)z.00.01.02.03.04.05.06.07.08.090.0.5000.5040.5080.5120.5160.5199.5239.5279.5319.53590.1.5398.5438.5478.5517.5557.5596.5636.5675.5714.57530.2.5793.5832.5871.5910.5948.5987.6026.6064.6103.61410.3.6179.6217.6255.6293.6331.6368.6406.6443.6480.65170.4.6554.6591.6628.6664.6700.6736.6772.6

44、808.6844.68790.5.6915.6950.6985.7019.7054.7088.7123.7157.7190.72240.6.7257.7291.7324.7357.7389.7422.7454.7486.7517.75490.7.7580.7611.7642.7673.7704.7734.7764.7794.7823.78520.8.7881.7910.7939.7967.7995.8023.8051.8078.8106.81330.9.8159.8186.8212.8238.8264.8289.8315.8340.8365.83891.0.8413.8438.8461.848

45、5.85088531.8554.8577.8599.86211.1.8643.8665.8686.8708.8729.8749.8770.8790.8810.88301.2.8849.8869.8888.8907.8925.8944.8962.8980.8997.90151.3.9032.9049.9066.9082.9099.9115.9131.9147.9162.91771.4.9192.9207.9222.9236.9251.9265.9279.9292.9306.93191.5.9332.9345.9357.9370.9382.9394.9406.9418.9429.94411.6.9

46、452.9463.9474.9484.9495.9505.9515.9525.9535.95451.7.9554.9564.9573.9582.9591.9599.9608.9616.9625.96331.8.9641.9649.9656.9664.9671.9678.9686.9693.9699.97061.9.9713.9719.9726.9732.9738.9744.9750.9756.9761.97672.0.9772.9778.9783.9788.97939798.9803.9808.9812.98172.1.9821.9826.9830.9834.9838.9842.9846.98

47、50.9854.98572.2.9861.9864.9868.9871.9875.9878.9881.9884.9887.98902.3.9893.9896.9898.9901.9904.9906.9909.9911.9913.99162.4.9918.9920.9922.9925.9927.9929.9931.9932.9934.99362.5.9938.9940.9941.9943.9945.9946.9948.9949.9951.99522.6.9953.9955.9956.9957.9959.9960.9961.9962.9963.99642.7.9965.9966.9967.9968

48、.9969.9970.9971.9972.9973.99742.8.9974.9975.9976.9977.9977.9978.9979.9979.9980.99812.9.9981.9982.9982.9983.9984.9984.9985.9985.9986.99863.0.9987.9987.9987.9988.99889989.9989.9989.9990.99903.1.9990.9991.9991.9991.9992.9992.9992.9992.9993.99933.2.9993.9993.9994.9994.9994.9994.9994.9995.9995.99953.3.99

49、95.9995.9995.9996.9996.9996.9996.9996.9996.99973.4.9997.9997.9997.9997.9997.9997.9997.9997.9997.99982018 AP® STATISTICS FREE-RESPONSE QUESTIONSProbability pTable entry for p and C is the point t* with probability p lying above it and probability C lying between t * and t*.t*Table B t distribution critical valuesdfTail probability p.0.05.025.02.01.005.0025.001.000511.0001.3761.9633.0786.31412.7115.8931.8263.66127.3318.3636.62.8161.0611.3861.8862.9204.3034.8496.9659.92514.0922.3331.603.765.9781.2501.6382.3533.1823.4824.5415.8417.45310.