Ria wants to know if there is a specific difference between the average monthly hair growth using Shampoo A vs Shampoo B. She recruited 8 participants and compared their average monthly hair growth (in centimeters) using two different brands. Her data is assumed to be normally distributed which produced the following values: Shampoo A0.50Shampoo B1.001.501.700.750.601.251.251.001.252.002.001.501.001.501.75 t Tablecum. probt soone-tail0.500.250.200.150.100.050.0250.010.0050.001 0.0005two-tails1.000.500.400.300.200.100.050.020.010.0020.001df120.0001.0001.3761.9633.0781.8866.31412.7131.8263.66318.31636.629.9255.8410.0000.8161.0611.3861.2502.9204.3036.96522.32731.59930.0000.7650.9781.6381.5332.3533.1824.54110.21512.92440.0000.7410.9411.1902.1322.0152.7763.7474.6047.1738.61050.0000.7270.9201.1563.3651.4761.4402.5714.0325.8936.8690.0000.7180.7110.9060.8961.1341.9432.4473.1433.7075.2085.9591.8951.8601.8332.9982.8962.8214.7854.5014.2970.0001.1191.4152.3652.3063.4995.40880.0000.7060.8891.1081.3973.3555.0410.0000.7030.8831.1001.3832.2623.2504.78122284.58710110.0000.7000.8791.0931.3721.3631.8121.7962.7643.1694.1440.0000.6970.8761.0882.2012.7183.1064.0254.437120.0000.6950.8731.0831.3561.7822.1792.6813.0553.9304.3180.0001.0791.0763.0122.977130.6940.8700.8681.3501.7712.1602.6503.8524.221140.0000.6921.3451.7612.1452.6243.7874.14015160.0000.6910.8661.0741.3411.7532.1312.6022.9473.7334.0730.0000.6900.8651.0711.3371.7462.1202.5832.9213.6864.015170.0000.6890.8631.0691.3331.3301.3281.3251.3231.7402.1102.5672.8983.6463.965180.0000.6880.8621.0671.7342.1012.5522.8783.6103.922190.0000.6880.8611.0661.7292.0932.5392.8613.5793.883200.0000.6870.8601.0641.7252.0862.0802.5282.8453.5523.8500.6860.6860.685210.0000.8591.0631.7212.5182.8313.5273.8190.0002.8192.807220.8581.0611.3211.7172.0742.5083.5053.4853.7923.7682.0692.064230.0000.8581.0601.3191.3181.7142.5001.0591.0580.8572.7972.787240.0000.6851.7112.4923.4673.7453.7253.707250.0000.6840.8561.3161.3151.7082.0602.4853.450260.0000.6840.8561.0581.7062.0562.4792.7793.4350.0001.0571.7031.701270.6840.8551.3142.0522.4732.7713.4213.4083.690280.0000.6830.8551.0561.3132.0482.4672.7633.674290.0000.6830.8541.0551.3111.6992.0452.4622.7563.3963.6590.8540.851300.0000.6831.0551.3101.6972.7502.0422.0212.4573.3853.646400.0000.6811.0501.3031.6842.4232.7043.3073.5510.0000.0000.8483.2323.195600.6791.0451.0431.2961.6712.0001.9901.9842.3902.6603.460800.6780.8461.2921.6642.3742.6393.4162.3642.3303.1743.0981000.0000.6770.8451.0421.2901.6602.6262.5813.39010000.0000.6750.8421.0371.2821.6461.9623.3000.0000.6740.8421.0361.2821.6451.9602.3262.5763.0903.2910%50%60%70%80%90%95%98%99% 99.8% 99.9%Confidence Levelt-table.xls 7/14/2007

Answered: Ria wants to know if there is a…

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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Related questions

Question

Ria wants to know if there is a specific difference between the average monthly hair growth using Shampoo A vs Shampoo B. She recruited 8 participants and compared their average monthly hair growth (in centimeters) using two different brands. Her data is assumed to be normally distributed which produced the following values:

Shampoo A
0.50
Shampoo B
1.00
1.50
1.70
0.75
0.60
1.25
1.25
1.00
1.25
2.00
2.00
1.50
1.00
1.50
1.75

t Table
cum. prob
t so
one-tail
0.50
0.25
0.20
0.15
0.10
0.05
0.025
0.01
0.005
0.001 0.0005
two-tails
1.00
0.50
0.40
0.30
0.20
0.10
0.05
0.02
0.01
0.002
0.001
df
1
2
0.000
1.000
1.376
1.963
3.078
1.886
6.314
12.71
31.82
63.66
318.31
636.62
9.925
5.841
0.000
0.816
1.061
1.386
1.250
2.920
4.303
6.965
22.327
31.599
3
0.000
0.765
0.978
1.638
1.533
2.353
3.182
4.541
10.215
12.924
4
0.000
0.741
0.941
1.190
2.132
2.015
2.776
3.747
4.604
7.173
8.610
5
0.000
0.727
0.920
1.156
3.365
1.476
1.440
2.571
4.032
5.893
6.869
0.000
0.718
0.711
0.906
0.896
1.134
1.943
2.447
3.143
3.707
5.208
5.959
1.895
1.860
1.833
2.998
2.896
2.821
4.785
4.501
4.297
0.000
1.119
1.415
2.365
2.306
3.499
5.408
8
0.000
0.706
0.889
1.108
1.397
3.355
5.041
0.000
0.703
0.883
1.100
1.383
2.262
3.250
4.781
2228
4.587
10
11
0.000
0.700
0.879
1.093
1.372
1.363
1.812
1.796
2.764
3.169
4.144
0.000
0.697
0.876
1.088
2.201
2.718
3.106
4.025
4.437
12
0.000
0.695
0.873
1.083
1.356
1.782
2.179
2.681
3.055
3.930
4.318
0.000
1.079
1.076
3.012
2.977
13
0.694
0.870
0.868
1.350
1.771
2.160
2.650
3.852
4.221
14
0.000
0.692
1.345
1.761
2.145
2.624
3.787
4.140
15
16
0.000
0.691
0.866
1.074
1.341
1.753
2.131
2.602
2.947
3.733
4.073
0.000
0.690
0.865
1.071
1.337
1.746
2.120
2.583
2.921
3.686
4.015
17
0.000
0.689
0.863
1.069
1.333
1.330
1.328
1.325
1.323
1.740
2.110
2.567
2.898
3.646
3.965
18
0.000
0.688
0.862
1.067
1.734
2.101
2.552
2.878
3.610
3.922
19
0.000
0.688
0.861
1.066
1.729
2.093
2.539
2.861
3.579
3.883
20
0.000
0.687
0.860
1.064
1.725
2.086
2.080
2.528
2.845
3.552
3.850
0.686
0.686
0.685
21
0.000
0.859
1.063
1.721
2.518
2.831
3.527
3.819
0.000
2.819
2.807
22
0.858
1.061
1.321
1.717
2.074
2.508
3.505
3.485
3.792
3.768
2.069
2.064
23
0.000
0.858
1.060
1.319
1.318
1.714
2.500
1.059
1.058
0.857
2.797
2.787
24
0.000
0.685
1.711
2.492
3.467
3.745
3.725
3.707
25
0.000
0.684
0.856
1.316
1.315
1.708
2.060
2.485
3.450
26
0.000
0.684
0.856
1.058
1.706
2.056
2.479
2.779
3.435
0.000
1.057
1.703
1.701
27
0.684
0.855
1.314
2.052
2.473
2.771
3.421
3.408
3.690
28
0.000
0.683
0.855
1.056
1.313
2.048
2.467
2.763
3.674
29
0.000
0.683
0.854
1.055
1.311
1.699
2.045
2.462
2.756
3.396
3.659
0.854
0.851
30
0.000
0.683
1.055
1.310
1.697
2.750
2.042
2.021
2.457
3.385
3.646
40
0.000
0.681
1.050
1.303
1.684
2.423
2.704
3.307
3.551
0.000
0.000
0.848
3.232
3.195
60
0.679
1.045
1.043
1.296
1.671
2.000
1.990
1.984
2.390
2.660
3.460
80
0.678
0.846
1.292
1.664
2.374
2.639
3.416
2.364
2.330
3.174
3.098
100
0.000
0.677
0.845
1.042
1.290
1.660
2.626
2.581
3.390
1000
0.000
0.675
0.842
1.037
1.282
1.646
1.962
3.300
0.000
0.674
0.842
1.036
1.282
1.645
1.960
2.326
2.576
3.090
3.291
0%
50%
60%
70%
80%
90%
95%
98%
99% 99.8% 99.9%
Confidence Level
t-table.xls 7/14/2007

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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