An SRS of 350 high school seniors gained an average of x¯=23.99 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation σ=49.49. We want to estimate the mean change in score μ in the population of all high school seniors.(a) Using the 68 – 95 – 99.7 Rule or the z-table (Table A), give a 68% confidence interval (a,b) for μ based on this sample.(Enter your answers rounded to three decimal places).a=b= (b) Based on your confidence interval in part (a), how certain are you that the mean change in score μ in the population of all high school seniors is greater than 0?A) We cannot be certain at all. If we want to make conclusions about the population mean change in score, we should do a hypothesis test instead of a confidence interval. B) The interval does not contain 0 , so we are 68% certain that the mean change in score in the population of all high school seniors is greater than 0. C) The entire interval is larger than 0 , so we are 68% certain that the mean change in score in the population of all high school seniors is greater than 0. D) The upper endpoint of the interval is larger than 0 , so we are 68% certain that the mean change in score in the population of all high school seniors is greater than 0. TABLES697Table entryTable entry for z is the area under thestandard Normal curve to the left of z.TABLE A Standard Normal cumulative proportions (continued).00.01.02.03.04.05.06.07.08.090.0.5000.5040.5080.5120.5160.5199.5239.5279.5319.5359.5557.5948.6331.5636.60260.1.5398.5438.5478.5517.5596.5675.5714.57530.2.5793.5832.5871.5910.5987.6064.6103.61410.30.4.6406.6772.6480.6844.6179.6217.6255.6293.6368.6443.6517.6554.6591.6628.6664.6700.6736.6808.6879.6950.7054.7389.7088.7422.7123.7454.77640.5.6915.6985.7019.7157.7190.72240.6.7257.7580.7517.7823.8106.7291.7324.7357.7486.7794.8078.8340.75490.7.7611.7642.7673.7704.7734.7852.8023.82890.8.7881.7910.7939.7967.7995.8051.81330.9.8159.8186.8212.8238.8264.8315.8365.8389.8485.8708.8907.8508.8577.87901.0.8413.8438.8461.8531.8554.8599.8621.8643.8849.8749.89441.1.8665.8686.8729.8770.8810.88301.2.8869.8888.8925.8962.8980.8997.90151.3.9032.9049.9066.9082.9099.9115.9131.9147.9162.91771.4.9192.9207.9222.9236.9251.9265.9279.9292.9306.93191.5.9332.9345.9357.9370.9382.9394.9406.9418.9429.9441.9463.95641.6.9452.9474.9484.9495.9505.9515.9525.9535.95451.7.9554.9573.9582.9591.9599.9608.9616.9625.9633.9678.97441.8.9641.9649.9656.9664.9671.9686.9693.9699.97061.9.9713.9719.9726.9732.9738.9750.9756.9761.97672.0.9772.9778.9783.9788.9793.9798.9803.9808.9812.98172.1.9821.9826.9830.9834.9838.9842.9846.9850.9854.9887.9913.98572.2.9861.9864.9868.9871.9875.9878.9881.9884.98902.3.9893.9896.9898.9901.9904.9906.9909.9911.99162.4.9918.9920.9922.9925.9927.9929.9931.9932.9934.99362.5.9938.9940.9941.9943.9945.9946.9948.9949.9951.99522.6.9953.9955.9956.9957.9959.9960.9961.9962.9963.99642.7.9965.9966.9967.9968.9969.9970.9971.9972.9973.9974.9977.99832.8.9974.9975.9976.9977.9978.9979.9979.9980.99812.9.9981.9982.9982.9984.9984.9985.99859986.99863.0.9987.9987.9987.99889988.9989.9989.9989.9990.99903.1.9990.9991.9991.9991.9992.9992.9992.9992.9993.99933.2.9993.9993.9994.9994.9994.9994.9994.9996.9995.9995.99953.3.9995.9995.9995.9996.9996.9996.9996.9996.99973.4.9997.9997.9997.9997.9997.9997.9997.9997.9997.9998 696TABLESTable entry for z is the area under theTable entrystandard Normal curve to the left of z.TABLE A Standard normal cumulative proportions.00.01.02.03.04.05.06.07.08.09-3.4.0003.0003.0003.0003.0003.0003.0003.0003.0003.0002.0003.0005.0007.0005.0004.0006-3.3.0005.0005.0004.0004.0004.0004.0004-3.2.0007.0007.0006.0006.0006.0006.0005.0005-3.1.0010.0009.0009.0009.0008.0008.0008.0008.0007-3.0.0013.0013.0013.0012.0012.0011.0011.0011.0010.0010-2.9.0019.0018.0018.0017.0016.0016.0015.0015.0014.0014.0023.0032-2.8.0026.0025.0024.0023.0022.0021.0021.0020.0019-2.7.0035.0034.0033.0031.0030.0029.0028.0027.0026-2.6.0047.0045.0044.0043.0041.0040.0054.0039.0038.0037.0036-2.5.0062.0060.0059.0057.0055.0052.0051.0049.0048-2.4.0064.0084.0082.0080.0078.0075.0073.0071.0069.0068.0066-2.3.0107.0104.0102.0099.0096.0094.0091.0089.0087-2.2.0139.0136.0132.0129.0125.0122.0119.0116.0113.0110.0174.0222.0170.0217-2.1.0179.0166.0162.0158.0154.0150.0146.0143-2.0.0228.0212.0207.0202.0197.0192.0188.0183.0274.0287.0359.0281.0268.0262.0256.0250.0233.0244.0307.0384-1.9.0239.0314- 1.8- 1.7.0336.0418.0516.0329.0409.0351.0344.0322.0301.0294.0446.0436.0427.0401.0392.0375.0367.0485.0505.0618.0455.0548.0668-1.6.0537.0526.0495.0475.0465-1.5.0655.0643.0630.0606.0594.0582.0571.0559-1.4-1.3.0694.0838.0808.0793.0778.0764.0749.0735.0721.0708.0681.0968.0951.0934.0918.0901.0885.0869.0853.0823- 1.2- 1.1.1038.1230.1151.1131.1112.1093.1075.1056.1020.1003.0985.1357.1335.1314.1292.1271.1251.1210.1190.1170-1.0.1587.1562.1539.1515.1492.1469.1446.1423.1401.1379.1814.2090-0.9.1841.1788.1762.1736.1711.1685.1660.1635.1611-0.8.2119.2061.2033.2005.1977.1949.1922.1894.1867-0.7.2420.2389.2358.2327.2296.2266.2236.2206.2177.2148-0.6.2743.2709.2676.2643.2611.2578.2546.2514.2483.2451-0.530853050.3015.2981.2946.2912.2877.2843.2810.2776.3409.3783.4168-0.4.3446.3372.33363300.3264.3228.3192.3156.3121-0.3.3821.37453707.3669.3632.3594.35573520.3483.4090.4483.4880-0.2.4207.4129.4052.4013.3974.3936.3897.3859.4404.4801.4247.4641-0.1.4602.4562.4522.4443.4364.4325.4286-0.0.5000.4960.4920.4840.4761.4721.4681

(a) From the given information, the value of mean is = 23.99. By using central limit theorem, a…

An SRS of 350 high school seniors gained an average of x¯=23.99 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation σ=49.49. We want to estimate the mean change in score μ in the population of all high school seniors. (a) Using the 68 – 95 – 99.7 Rule or the z-table (Table A), give a 68% confidence interval (a,b) for μ based on this sample. (Enter your answers rounded to three decimal places). a= b= (b) Based on your confidence interval in part (a), how certain are you that the mean change in score μ in the population of all high school seniors is greater than 0? A) We cannot be certain at all. If we want to make conclusions about the population mean change in score, we should do a hypothesis test instead of a confidence interval. B) The interval does not contain 0 , so we are 68% certain that the mean change in score in the population of all high school seniors is greater than 0. C) The entire interval is larger than 0 , so we are 68% certain that the mean change in score in the population of all high school seniors is greater than 0. D) The upper endpoint of the interval is larger than 0 , so we are 68% certain that the mean change in score in the population of all high school seniors is greater than 0.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

An SRS of 350 high school seniors gained an average of x¯=23.99 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation σ=49.49. We want to estimate the mean change in score μ in the population of all high school seniors.

(a) Using the 68 – 95 – 99.7 Rule or the z-table (Table A), give a 68% confidence interval (a,b) for μ based on this sample.

(Enter your answers rounded to three decimal places).

(b) Based on your confidence interval in part (a), how certain are you that the mean change in score μ in the population of all high school seniors is greater than 0?

A) We cannot be certain at all. If we want to make conclusions about the population mean change in score, we should do a hypothesis test instead of a confidence interval.

B) The interval does not contain 0 , so we are 68% certain that the mean change in score in the population of all high school seniors is greater than 0.

C) The entire interval is larger than 0 , so we are 68% certain that the mean change in score in the population of all high school seniors is greater than 0.

D) The upper endpoint of the interval is larger than 0 , so we are 68% certain that the mean change in score in the population of all high school seniors is greater than 0.

TABLES
697
Table entry
Table entry for z is the area under the
standard Normal curve to the left of z.
TABLE A Standard Normal cumulative proportions (continued)
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
0.0
.5000
.5040
.5080
.5120
.5160
.5199
.5239
.5279
.5319
.5359
.5557
.5948
.6331
.5636
.6026
0.1
.5398
.5438
.5478
.5517
.5596
.5675
.5714
.5753
0.2
.5793
.5832
.5871
.5910
.5987
.6064
.6103
.6141
0.3
0.4
.6406
.6772
.6480
.6844
.6179
.6217
.6255
.6293
.6368
.6443
.6517
.6554
.6591
.6628
.6664
.6700
.6736
.6808
.6879
.6950
.7054
.7389
.7088
.7422
.7123
.7454
.7764
0.5
.6915
.6985
.7019
.7157
.7190
.7224
0.6
.7257
.7580
.7517
.7823
.8106
.7291
.7324
.7357
.7486
.7794
.8078
.8340
.7549
0.7
.7611
.7642
.7673
.7704
.7734
.7852
.8023
.8289
0.8
.7881
.7910
.7939
.7967
.7995
.8051
.8133
0.9
.8159
.8186
.8212
.8238
.8264
.8315
.8365
.8389
.8485
.8708
.8907
.8508
.8577
.8790
1.0
.8413
.8438
.8461
.8531
.8554
.8599
.8621
.8643
.8849
.8749
.8944
1.1
.8665
.8686
.8729
.8770
.8810
.8830
1.2
.8869
.8888
.8925
.8962
.8980
.8997
.9015
1.3
.9032
.9049
.9066
.9082
.9099
.9115
.9131
.9147
.9162
.9177
1.4
.9192
.9207
.9222
.9236
.9251
.9265
.9279
.9292
.9306
.9319
1.5
.9332
.9345
.9357
.9370
.9382
.9394
.9406
.9418
.9429
.9441
.9463
.9564
1.6
.9452
.9474
.9484
.9495
.9505
.9515
.9525
.9535
.9545
1.7
.9554
.9573
.9582
.9591
.9599
.9608
.9616
.9625
.9633
.9678
.9744
1.8
.9641
.9649
.9656
.9664
.9671
.9686
.9693
.9699
.9706
1.9
.9713
.9719
.9726
.9732
.9738
.9750
.9756
.9761
.9767
2.0
.9772
.9778
.9783
.9788
.9793
.9798
.9803
.9808
.9812
.9817
2.1
.9821
.9826
.9830
.9834
.9838
.9842
.9846
.9850
.9854
.9887
.9913
.9857
2.2
.9861
.9864
.9868
.9871
.9875
.9878
.9881
.9884
.9890
2.3
.9893
.9896
.9898
.9901
.9904
.9906
.9909
.9911
.9916
2.4
.9918
.9920
.9922
.9925
.9927
.9929
.9931
.9932
.9934
.9936
2.5
.9938
.9940
.9941
.9943
.9945
.9946
.9948
.9949
.9951
.9952
2.6
.9953
.9955
.9956
.9957
.9959
.9960
.9961
.9962
.9963
.9964
2.7
.9965
.9966
.9967
.9968
.9969
.9970
.9971
.9972
.9973
.9974
.9977
.9983
2.8
.9974
.9975
.9976
.9977
.9978
.9979
.9979
.9980
.9981
2.9
.9981
.9982
.9982
.9984
.9984
.9985
.9985
9986
.9986
3.0
.9987
.9987
.9987
.9988
9988
.9989
.9989
.9989
.9990
.9990
3.1
.9990
.9991
.9991
.9991
.9992
.9992
.9992
.9992
.9993
.9993
3.2
.9993
.9993
.9994
.9994
.9994
.9994
.9994
.9996
.9995
.9995
.9995
3.3
.9995
.9995
.9995
.9996
.9996
.9996
.9996
.9996
.9997
3.4
.9997
.9997
.9997
.9997
.9997
.9997
.9997
.9997
.9997
.9998

696
TABLES
Table entry for z is the area under the
Table entry
standard Normal curve to the left of z.
TABLE A Standard normal cumulative proportions
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
-3.4
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0002
.0003
.0005
.0007
.0005
.0004
.0006
-3.3
.0005
.0005
.0004
.0004
.0004
.0004
.0004
-3.2
.0007
.0007
.0006
.0006
.0006
.0006
.0005
.0005
-3.1
.0010
.0009
.0009
.0009
.0008
.0008
.0008
.0008
.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
.0023
.0032
-2.8
.0026
.0025
.0024
.0023
.0022
.0021
.0021
.0020
.0019
-2.7
.0035
.0034
.0033
.0031
.0030
.0029
.0028
.0027
.0026
-2.6
.0047
.0045
.0044
.0043
.0041
.0040
.0054
.0039
.0038
.0037
.0036
-2.5
.0062
.0060
.0059
.0057
.0055
.0052
.0051
.0049
.0048
-2.4
.0064
.0084
.0082
.0080
.0078
.0075
.0073
.0071
.0069
.0068
.0066
-2.3
.0107
.0104
.0102
.0099
.0096
.0094
.0091
.0089
.0087
-2.2
.0139
.0136
.0132
.0129
.0125
.0122
.0119
.0116
.0113
.0110
.0174
.0222
.0170
.0217
-2.1
.0179
.0166
.0162
.0158
.0154
.0150
.0146
.0143
-2.0
.0228
.0212
.0207
.0202
.0197
.0192
.0188
.0183
.0274
.0287
.0359
.0281
.0268
.0262
.0256
.0250
.0233
.0244
.0307
.0384
-1.9
.0239
.0314
- 1.8
- 1.7
.0336
.0418
.0516
.0329
.0409
.0351
.0344
.0322
.0301
.0294
.0446
.0436
.0427
.0401
.0392
.0375
.0367
.0485
.0505
.0618
.0455
.0548
.0668
-1.6
.0537
.0526
.0495
.0475
.0465
-1.5
.0655
.0643
.0630
.0606
.0594
.0582
.0571
.0559
-1.4
-1.3
.0694
.0838
.0808
.0793
.0778
.0764
.0749
.0735
.0721
.0708
.0681
.0968
.0951
.0934
.0918
.0901
.0885
.0869
.0853
.0823
- 1.2
- 1.1
.1038
.1230
.1151
.1131
.1112
.1093
.1075
.1056
.1020
.1003
.0985
.1357
.1335
.1314
.1292
.1271
.1251
.1210
.1190
.1170
-1.0
.1587
.1562
.1539
.1515
.1492
.1469
.1446
.1423
.1401
.1379
.1814
.2090
-0.9
.1841
.1788
.1762
.1736
.1711
.1685
.1660
.1635
.1611
-0.8
.2119
.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
.3409
.3783
.4168
-0.4
.3446
.3372
.3336
3300
.3264
.3228
.3192
.3156
.3121
-0.3
.3821
.3745
3707
.3669
.3632
.3594
.3557
3520
.3483
.4090
.4483
.4880
-0.2
.4207
.4129
.4052
.4013
.3974
.3936
.3897
.3859
.4404
.4801
.4247
.4641
-0.1
.4602
.4562
.4522
.4443
.4364
.4325
.4286
-0.0
.5000
.4960
.4920
.4840
.4761
.4721
.4681

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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