A class survey in a large class for first‑year college students asked, “About how many hours do you study during a typical week?” The mean response of the 463 students was x¯=13.7 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation σ=7.4 hours in the population of all first‑year students at this university.Regard these students as an SRS from the population of all first‑year students at this university. Does the study give good evidence that students claim to study more than 13 hours per week on the average?You may find Table A helpful.(a) State null and alternative hypotheses in terms of the mean study time in hours for the population. A) H0:μ=13 hours ; Ha:μ≠13 hours B) H0:μ=13 hours ; Ha:μ>13 hours C) H0:μ=13 hours ; Ha:μ=13 hours D) H0:μ=13 hours ; Ha:μ<13 hours (b) What is the value of the test statistic z ? (Enter your answer rounded to two decimal places.) z= (c) What is the P ‑value of the test? A) larger than 0.05B) between 0.020 and 0.030C) between 0.001 and 0.005D) less than 0.0001 Can you conclude that students do claim to study more than 13 hours per week on average? A) Yes, the large P ‑value is strong evidence that students do claim to study more than 13 hours per week on average. B) Yes, the small P ‑value is strong evidence that students do claim to study more than 13 hours per week on average. C) No, the large P ‑value is strong evidence that students do not claim to study more than 13 hours per week on average. D) No, the small P ‑value is strong evidence that students do not claim to study more than 13 hours per week on average. 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

Given Data: x¯=13.7 σ=7.4 n=463 a) Null and Alternate Hypothesis: B) H0:μ=13 hours ; Ha:μ>13…

Answered: A class survey in a large class for…

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

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A class survey in a large class for first‑year college students asked, “About how many hours do you study during a typical week?” The mean response of the 463 students was x¯=13.7 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation σ=7.4 hours in the population of all first‑year students at this university.

Regard these students as an SRS from the population of all first‑year students at this university. Does the study give good evidence that students claim to study more than 13 hours per week on the average?

You may find Table A helpful.

(a) State null and alternative hypotheses in terms of the mean study time in hours for the population.

A) H0:μ=13 hours ; Ha:μ≠13 hours

B) H0:μ=13 hours ; Ha:μ>13 hours

C) H0:μ=13 hours ; Ha:μ=13 hours

D) H0:μ=13 hours ; Ha:μ<13 hours

(b) What is the value of the test statistic z ? (Enter your answer rounded to two decimal places.)

(c) What is the P ‑value of the test?

A) larger than 0.05

B) between 0.020 and 0.030

C) between 0.001 and 0.005

D) less than 0.0001

Can you conclude that students do claim to study more than 13 hours per week on average?

A) Yes, the large P ‑value is strong evidence that students do claim to study more than 13 hours per week on average.

B) Yes, the small P ‑value is strong evidence that students do claim to study more than 13 hours per week on average.

C) No, the large P ‑value is strong evidence that students do not claim to study more than 13 hours per week on average.

D) No, the small P ‑value is strong evidence that students do not claim to study more than 13 hours per week on average.

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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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