Question: Researchers from a certain country were interested in how characteristics of the spleen of residents in their tropical environment compare to those found elsewhere in the world. The researchers randomly sampled 92 males and 108 females in their country. The mean and standard deviation of the spleen lengths for the males were 11.4cm and 0.9cm, respectively, and those for the females were 10.1cm and 1.1cm, respectively. Determine a 99% confidence interval for the difference between mean spleen lengths of males and females in this country. Let population 1 be all males in the country and let population 2 be all females in the country. The 99% confidence interval for μ1−μ2 is ( [ ],[ ] ). (Round to three decimal places as needed. Use ascending order.)
Question: Researchers from a certain country were interested in how characteristics of the spleen of residents in their tropical environment compare to those found elsewhere in the world. The researchers randomly sampled 92 males and 108 females in their country. The mean and standard deviation of the spleen lengths for the males were 11.4cm and 0.9cm, respectively, and those for the females were 10.1cm and 1.1cm, respectively. Determine a 99% confidence interval for the difference between mean spleen lengths of males and females in this country. Let population 1 be all males in the country and let population 2 be all females in the country. The 99% confidence interval for μ1−μ2 is ( [ ],[ ] ). (Round to three decimal places as needed. Use ascending order.)
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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100%
Question:
Researchers from a certain country were interested in how characteristics of the spleen of residents in their tropical environment compare to those found elsewhere in the world. The researchers randomly sampled 92 males and 108 females in their country. The mean and standard deviation of the spleen lengths for the males were 11.4cm and 0.9cm, respectively, and those for the females were 10.1cm and 1.1cm, respectively. Determine a 99% confidence interval for the difference between mean spleen lengths of males and females in this country.
Let population 1 be all males in the country and let population 2 be all females in the country.
The 99% confidence interval for μ1−μ2 is ( [ ],[ ] ).
(Round to three decimal places as needed. Use ascending order.)
(Please ready carefully and check calculations) Have been having so much issues with this. Posted two questions already but none helped. :^(
P.S: I added a sample problem that provides sample steps.
Transcribed Image Text:Sample
Researchers from a certain country were interested in how characteristics of the spleen of residents in their
tropical environment compare to those found elsewhere in the world. The researchers randomly sampled 96
males and 104 females in their country. The mean and standard deviation of the spleen lengths for the males
were 11.5 cm and 0.7 cm, respectively, and those for the females were 10.6 cm and 0.7 cm, respectively.
Determine a 95% confidence interval for the difference between mean spleen lengths of males and females in
this country.
Click here to view page 1 of the table of critical values of t.
Click here to view page 2 of the table of critical values of t.
The endpoints of the confidence interval for u, -H, are given by the formula below, where s, is the pooled
sample standard deviation, t,/2 is found with df =n, +n, -2, x, and x, are the means of samples 1 and 2,
respectively, and n, and n, are the sizes of samples 1 and 2, respectively.
For a confidence level of 1-a, use a t-distribution table to find t,2 with df = n, + n, - 2. Note that the
confidence level is equal to 1-a when it is written as a decimal. Determine the value of a.
1-a = 0.95
a = 0.05
Now compute the degrees of freedom. Let population 1 be all males in the country and let population 2 be all
females in the country.
df = n, + n2 - 2
= 96 + 104 - 2
= 198
Next determine t, using a t-distribution table, where df = 198 and a = 0.05. Since there is no row for
df = 198 in the given t-distribution table, use the next closest entry in the table with df less than 198, which, in
this case, is df = 100.
tal2 = to.05/2
= to.025
= 1.984
The formula for s, is shown below.
(n, - 1)s? + (n2 - 1) s
S, =
n, +n2 -2
Substitute the known values into the formula for s, and simplify.
(96 - 1)(0.7)2 + (104 - 1)(0.7)?
s, =
= 0.7
96 + 104 - 2
Next substitute the known values as well as s, = 0.7 and t/2 = 1.984 into the formula for the endpoints of the
confidence interval and simplify, rounding to three decimal places as needed.
(11.5 - 10.6) ± 1.984 • 0.7
96
= 0.9
0.197
The endpoints of the confidence interval for u, - H, are 0.9+0.197. Thus, the 95% confidence interval is
from 0.703 to 1.097.
Transcribed Image Text:df
10.10
10.01
10.005
df
6.314
df
fo.10
teas
10.025
df
3.078
1.886
12.706
4.303
31.821
63.657
2.920
6.965
9.925
50
1.299
1.298
1.676
1.675
1.638
2.353
3.182
4.541
5.841
3
2.009
2.403
2.678
50
1.533
2.132
2.776
3.747
4,604
2.008
2.402
2.676
51
2.007
2.674
2.672
52
1.298
1.675
2.400
52
1.476
1.440
1.415
2.015
1.943
1.895
2.571
3.365
4.032
3.707
3.499
53
1.298
1.674
2.006
2.399
53
6.
2.447
3.143
6.
54
1.297 1.674
2.005
2.397
2.670
54
7
2.365
2.306
2.262
2.998
2.896
7
1.397
1.860
3.355
55
1.297
1.673
2.004
2.396
2.668
55
9
1.383
1.833
2.821
3.250
9
56
1.297
1.673
2.003
2.395
2.667
56
2.665
2.663
2.662
57
1.297
1.672
1.672
1.671
10
1.372
2.002
2.394
57
1.812
1.796
2.228
2.764
3.169
10
58
1.296
1.296
2.002
2.001
2.392
2.391
11
58
1.363
1.356
1.350
1.345
2.201
2.718
3.106
11
12
1.782
2.179
2.681
3.055
12
59
59
13
1.771
2.160
2.650
3.012
13
60
1.296 1.671
2.000
2.390
2.660
60
14
1.761
2.145
2.624
2.977
14
61
1.296
1.295
1.295
1.295
1.670
2.000
2.389
2.659
61
15
1.341
1.753
2.131
2.602
2.583
2.947
2.921
15
16
62
1.670
1.999
2.388
2.657
62
16
1.337
1.746
2.120
63
1.669
1.998
2.387
2.386
2.656
63
17
1.333
1.740
2.110
2.567
2.898
17
64
1.669
1.998
2.655
64
1.330
1.734
2.552
2.539
18
2.101
2.093
2.878
2.861
18
1.997
1.997
65
1.295
1.295
1.669
2.385
2.384
2.654
2.652
19
1.328
1.729
19
65
66
1.668
66
20
21
1.325
1.725
2.086
2.528
2.845
20
67
1.294
1.668
1.996
1.995
1.995
2.383
2.651
67
1.323
1.321
1.721
2.080
2.074
2.518
2.508
2.831
2.819
21
68
1.294
1.668
2.382
2.650
68
22
1.717
22
69
1.294
1.667
2.382
2.649
69
23
1.319
1.714
2.069
2.500
2.807
23
24
1.318
1.711
2.064
2.492
2.797
24
70
1.294
1.667
1.994
2.381
2.648
70
25
1.316
1.708
2.060
2.485
2.787
25
71
1.294
1.667
1.994
2.380
2.647
71
72
1.293
1.666
2.379
2.646
72
1.315
1.314
1.993
1.993
2.379
1.993 2.378
26
1.706
2.056
2.479
2.779
26
1.666
1.666
73
1.293
2.645
73
74
27
1.703
2.052
2.473
2.771
2.763
27
74
1.293
2.644
2.048
2.045
28
1.313
1.701
1.699
2.467
28
29
1.311
2.462
2.756
29
75
1.293
1.292
1.292
1.665
1.664
1.663
1.992 2.377
2.643
75
1.310
1.697
2.042
2.457
2.750
30
80
85
1.990 2.374
2.639
2.635
80
85
30
31
1.309
1.696
2.040
1.988
2.371
2.453
2.449
2.445
2.744
2.738
2.733
31
32
1.694
1.309
1.308
2.037
2.035
32
33
90
1.291
1.662
1.987
2.368
2.632
90
33
1.692
95
1.291
1.661
1.985
2.366
2.629
95
34
1.307
1.691
2.032
2.441
2.728
34
100
1.290
1.660
1.984
2.364
2.626
100
35
1.306
1.690
2.030
2.438
2.724
35
200
1.286
1.653
1.972
2.345
2.601
200
36
1.306
1.688
2.028
2.434
2.719
36
300
1.284
1.650
1.968
2.339
2.592
300
1.687
2.026
2.024
37
1.305
2.431
2.715
37
400
1.284
1.649
1.966
2.336
2.588
400
38
1.304
1.686
2.429
2.712
2.708
38
500
1.283
1.648
1.965
2.334
2.586
500
39
1.304
1.685
2.023
2.426
39
600
1.283
1.647
1.964
2.333
2.584
600
40
1.303
1.303
1.302
1.302
1.684
2.021
2.423
2.704
40
700
1.283
1.647
1.963
2.332
2.583
700
41
1.683
2.020
2.421
2.701
41
800
1.283
1.282
1.647
1.963
2.331
2.330
2.582
2.581
800
1.682
1.681
2.018
2.017
42
2.418
2.698
42
1.647
1.963
1.962
1.961 2.328
43
2.416
900
900
2.695
2.692
43
44
1.301
1.680
2.015
2.414
44
1000
1.282
1.646
2.330
2.581
1000
2000
1.282
1.646
2.578
2000
45
1.301
1.679
2.014
2.013
2.412
2.690
2.687
45
46
1.300
1.679
2.410
46
df
f0.025
df
47
1.300
1.678
2.012
2.408
2.685
47
1.677
2.407
48
49
48
1.299
2.011
2.010
2.682
2.680
49
1.299
1.677
2.405
1.282
1.645
1.960 2.326 2.576
df
df
Za.10
%23
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