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:
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:
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 54E: Conditional probability If 40 of the population have completed college, and 85 of college graduates...
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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:
Transcribed Image Text: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
Transcribed Image Text: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
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