You are presented with the weights of 25 Cougars that has a mean weight of 100 lb with standard deviation of 25 lb. Scientists hypothesized that this group belong to the female Cougars with reference weight of 75 lb.  Can you test using statistical framework whether this is true or not (with alpha of 0.05).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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You are presented with the weights of 25 Cougars that has a mean weight of 100 lb with standard deviation of 25 lb. Scientists hypothesized that this group belong to the female Cougars with reference weight of 75 lb. 

Can you test using statistical framework whether this is true or not (with alpha of 0.05).

Make use of the table below to know the p-value of your test statistic.

 

d.f.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
60
120
∞
PROBABILITY
0.1
0.05
0.02 0.01 0.001
6.314 12.706 31.821
63.657
636.619
2.920
4.303 6.965
9.925
31.598
2.353
3.182 4.541
5.841
12.941
2.132
2.776
3.747 4.604
8.610
2.015 2.571
3.365
4.032
6.859
0.718 1.943 2.447
3.143
3.707
5.959
0.711
1.895 2.365
2.998
3.499
5.405
0.706
1.860
2.306
2.896
3.355
5.041
0.703 1.833
2.262 2.821
3.250
4.781
0.700
1.812
2.228
2.764
3.169
4.587
0.697 1.796 2.201
2.718
3.106 4.437
1.782
2.179
2.681 3.055 4.318
1.771 2.160
2.650
3.012
4.221
2.145
2.624 2.977
4.140
2.131 2.602 2.947
4.073
2.120 2.583
2.921
4.015
2.110
2.567 2.898
3.965
1.734 2.101
2.552
2.878
3.922
2.093
2.539
2.861
3.883
2.086
2.528
2.845
3.850
2.080 2.518
2.831
3.819
2.508
2.819
3.792
2.500
2.807
3.767
2.797
2.787
0.5
1.000
0.816
0.765
0.741
0.727
0.695
0.694
0.692 1.761
0.691
1.753
0.690 1.746
0.689 1.740
0.688
0.688 1.729
0.687
1.725
0.686 1.721
0.686
0.685
0.685
1.711 2.064
2.492
0.684
1.708
2.060
2.485
0.684
1.706
2.056 2.479
0.684
1.703 2.052
2.473
0.684
1.701
2.048
2.467
2.763
0.683
1.699
2.045
2.462 2.756
0.683
1.697
2.042
0.681
1.684
2.021
0.679
1.671
2.000
0.677 1.658
1.980
0.674 1.645 1.960
1.717 2.074
1.714
2.069
2.779
2.771
2.457
2.750
2.423 2.704
2.390
2.660
2.358
2.617
2.326
2.576
3.745
3.725
3.707
3.690
3.674
3.659
3.646
3.551
3.460
3.373
3.291
Transcribed Image Text:d.f. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 ∞ PROBABILITY 0.1 0.05 0.02 0.01 0.001 6.314 12.706 31.821 63.657 636.619 2.920 4.303 6.965 9.925 31.598 2.353 3.182 4.541 5.841 12.941 2.132 2.776 3.747 4.604 8.610 2.015 2.571 3.365 4.032 6.859 0.718 1.943 2.447 3.143 3.707 5.959 0.711 1.895 2.365 2.998 3.499 5.405 0.706 1.860 2.306 2.896 3.355 5.041 0.703 1.833 2.262 2.821 3.250 4.781 0.700 1.812 2.228 2.764 3.169 4.587 0.697 1.796 2.201 2.718 3.106 4.437 1.782 2.179 2.681 3.055 4.318 1.771 2.160 2.650 3.012 4.221 2.145 2.624 2.977 4.140 2.131 2.602 2.947 4.073 2.120 2.583 2.921 4.015 2.110 2.567 2.898 3.965 1.734 2.101 2.552 2.878 3.922 2.093 2.539 2.861 3.883 2.086 2.528 2.845 3.850 2.080 2.518 2.831 3.819 2.508 2.819 3.792 2.500 2.807 3.767 2.797 2.787 0.5 1.000 0.816 0.765 0.741 0.727 0.695 0.694 0.692 1.761 0.691 1.753 0.690 1.746 0.689 1.740 0.688 0.688 1.729 0.687 1.725 0.686 1.721 0.686 0.685 0.685 1.711 2.064 2.492 0.684 1.708 2.060 2.485 0.684 1.706 2.056 2.479 0.684 1.703 2.052 2.473 0.684 1.701 2.048 2.467 2.763 0.683 1.699 2.045 2.462 2.756 0.683 1.697 2.042 0.681 1.684 2.021 0.679 1.671 2.000 0.677 1.658 1.980 0.674 1.645 1.960 1.717 2.074 1.714 2.069 2.779 2.771 2.457 2.750 2.423 2.704 2.390 2.660 2.358 2.617 2.326 2.576 3.745 3.725 3.707 3.690 3.674 3.659 3.646 3.551 3.460 3.373 3.291
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