Ria wants to know if there is a significant difference between the aaverage monthly hair growth using Shampoo A vs Shampoo B. She recruited eight participants and compared their average monthly hair growth (in centimeters) using the two different brands. Her data is assumed to be normally distributed which produced the following values: Shampoo A 0.50 1.00 1.50 1.70 0.75 0.60 1.25 1.25 Shampoo B 1.00 1.25 2.00 2.00 1.50 1.00 1.50 1.75 Choose the appropriate test statistic and make a conclusion about the problem. Show your output below in a step-by-step manner: 21-22. State the null and alternative hypotheses 23-48. Make a decision about the null hypothesis: (23- 26) Calculate the degree of freedom. (27.) Assume that a.05 (two-tailed). Identify the critical values and state a decision rule.
Ria wants to know if there is a significant difference between the aaverage monthly hair growth using Shampoo A vs Shampoo B. She recruited eight participants and compared their average monthly hair growth (in centimeters) using the two different brands. Her data is assumed to be normally distributed which produced the following values: Shampoo A 0.50 1.00 1.50 1.70 0.75 0.60 1.25 1.25 Shampoo B 1.00 1.25 2.00 2.00 1.50 1.00 1.50 1.75 Choose the appropriate test statistic and make a conclusion about the problem. Show your output below in a step-by-step manner: 21-22. State the null and alternative hypotheses 23-48. Make a decision about the null hypothesis: (23- 26) Calculate the degree of freedom. (27.) Assume that a.05 (two-tailed). Identify the critical values and state a decision rule.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
Related questions
Question
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
Transcribed Image Text:Ria wants to know if there is a significant difference between the average monthly hair growth
using Shampoo A vs Shampoo B. She recruited eight participants and compared their average
monthly hair growth (in centimeters) using the two different brands. Her data is assumed to be
normally distributed which produced the following values:
Shampoo A
0.50
1.00
1.50
1.70
0.75
0.60
1.25
1.25
Shampoo B
1.00
1.25
2.00
2.00
1.50
1.00
1.50
1.75
Choose the appropriate test statistic and make a conclusion about the problem. Show your output
below in a step-by-step manner:
21 - 22. State the null and alternative hypotheses.
23- 48. Make a decision about the null hypothesis:
(23 - 26) Calculate the degree of freedom
(27.) Assume that a 05 (two-tailed). Identify the critical values and state a decision rule.
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