Question

The data shown below came from an experiment in which a grip dynamometer was used to obtain an estimate of the grip capabilities of males and females at two settings. Female Sample Male Sample Gen Setting 1 Setting 2 Differ Gen Setting 1 Setting 2 Differ S1-S2 S1-S2 M1 65 96 -31 F1 49 71 -22 M2 65 102 -37 F2 47 60 -13 M3 90 136 -46 F3 31 49 -18 M4 125 124 1 F4 32 61 -29 M5 82 116 -34 F5 56 71 -15 M6 95 120 -25 F6 40 70 -30 M7 60 127 -67 F7 30 61 -31 M8 61 72 -11 F8 50 70 -20 M9 49 60 -11 F9 30 85 -55 M10 62 107 -45 F10 52 80 -28 M11 74 130 -56 F11 65 70 -5 Assuming that the data came from normally distributed populations, answer the following questions: a) (10 points) Is there a statistically significant difference in the overall results observed for the two settings and if so which one appears to provide higher results? b) (10 points) Assuming equal variances for males and females, is there statistical evidence to show a statistically significant dissimilarity between the male and female observed differences in the two grip strength settings?

          The data shown below came from an experiment in which a grip dynamometer was used to obtain an estimate of the
grip capabilities of males and females at two settings.
Female Sample
Male Sample
Gen
Setting 1 Setting 2 Differ
Gen Setting 1 Setting 2 Differ
S1-S2
S1-S2
M1
65
96
-31
F1
49
71
-22
M2
65
102
-37
F2
47
60
-13
M3
90
136
-46
F3
31
49
-18
M4
125
124
1
F4
32
61
-29
M5
82
116
-34
F5
56
71
-15
M6
95
120
-25
F6
40
70
-30
M7
60
127
-67
F7
30
61
-31
M8
61
72
-11
F8
50
70
-20
M9
49
60
-11
F9
30
85
-55
M10
62
107
-45
F10
52
80
-28
M11
74
130
-56
F11
65
70
-5
Assuming that the data came from normally distributed populations, answer the following questions: a) (10 points) Is
there a statistically significant difference in the overall results observed for the two settings and if so which one
appears to provide higher results? b) (10 points) Assuming equal variances for males and females, is there statistical
evidence to show a statistically significant dissimilarity between the male and female observed differences in the two
grip strength settings?

Show more…

The data shown below came from an experiment in which a grip dynamometer was used to obtain an estimate of the
grip capabilities of males and females at two settings.
Female Sample
Male Sample
Gen
Setting 1 Setting 2 Differ
Gen Setting 1 Setting 2 Differ
S1-S2
S1-S2
M1
65
96
-31
F1
49
71
-22
M2
65
102
-37
F2
47
60
-13
M3
90
136
-46
F3
31
49
-18
M4
125
124
1
F4
32
61
-29
M5
82
116
-34
F5
56
71
-15
M6
95
120
-25
F6
40
70
-30
M7
60
127
-67
F7
30
61
-31
M8
61
72
-11
F8
50
70
-20
M9
49
60
-11
F9
30
85
-55
M10
62
107
-45
F10
52
80
-28
M11
74
130
-56
F11
65
70
-5
Assuming that the data came from normally distributed populations, answer the following questions: a) (10 points) Is
there a statistically significant difference in the overall results observed for the two settings and if so which one
appears to provide higher results? b) (10 points) Assuming equal variances for males and females, is there statistical
evidence to show a statistically significant dissimilarity between the male and female observed differences in the two
grip strength settings?

Added by Tyler N.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

07/31/2024

Step 1

First, we need to find the mean difference for both male and female samples. Let's denote the mean difference for males as $\bar{d_m}$ and for females as $\bar{d_f}$. Show more…

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Thanks for your feedback!

The data shown below came from an experiment in which a grip dynamometer was used to obtain an estimate of the grip capabilities of males and females at two settings. Assuming that the data came from normally distributed populations, answer the following questions: a) (10 points) Is there a statistically significant difference in the overall results observed for the two settings and if so, which one appears to provide higher results? b) (10 points) Assuming equal variances for males and females, is there statistical evidence to show a statistically significant dissimilarity between the male and female observed differences in the two grip strength settings?

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Transcript

00:02 So we are given that the data shown below came from the experiment in which the grip dynamometer was used to obtain the estimate of great capabilities for men two settings so these are what the ratings sequence you can see for setting one setting two for male sample and for female sample setting one and setting two and their difference are s one minus so according to first part of this question, is there is a statistical significant difference in overall result observed for two settings.

00:43 At significance level of alpha, we say 0 .05 if not given.

00:48 So let's get started to solutions.

00:50 First of all, we set the null haptasis for mu -d equals to 0.

00:56 Because obviously we are going to perform the haptitis first for mean difference.

01:01 Similarly, the alternative hypothesis will become moody not equals to 0.

01:06 This means to say we have to perform two tell data for paired t test.

01:12 So first of all, the most important is to find the mean setting 1, which can be calculated as summation of xith over n.

01:23 Now see, according to a part, we have to find this mean and all the terms for overall data.

01:31 Overall data means to say you need to find the submission of setting one for male, submission of setting one for female, combine both of them, and then find the mean of combined data.

01:44 So let me just write down some important things, that is, submission of men setting first.

01:54 This you will get 8 to 8 .8 submission of female setting 1, 4, 8 ,2 ,000.

02:01 So here 828 plus 482 divided by 11 plus 11.

02:08 So sample size would be 72.

02:12 So after dividing the mean which comes for setting 1 .59 .545.

02:19 Similarly, the submission of male setting to 1 .070.

02:26 Submission of female setting to 748.

02:32 Means what i am doing here i'm just taking the summation of this columns.

02:36 So you will get the mean setting add to submission of let's say the setting 2 is nothing but y by n.

02:47 So this will be goes to 1070 plus 748 divided by 22 so it will comes out equals to 88 .09.

03:02 Now similarly you will we will try to calculate mean for setting 1 minus setting 2 means the difference.

03:12 So by using the same formula it will come negative of 28 .2 545...

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