95% Confidence Interval.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Confidence interval with t-value [Refer to Module 10a slides for an example]
We want to find out if college students trust a presidential candidate (in this case Mitt Romney). We randomly select 29 college students from a national registry (assuming there was such a thing) and ask them to rate how trustworthy they find Mitt Romney on a scale of 0 to 7 with 0 being completely untrustworthy and 7 being completely trustworthy. The sample of 29 students results in an average of 3.94 points. We will also assume a sample standard deviation (sigma) of 2 points.
Using Table C from the text or the one pasted below, determine what the "t" value should be for a 95% Confidence Interval.
Then use the formula below to calculate a 95% confidence interval for college students level of trust of Mitt Romney. Show your work and/or describe the process you used to find the answer.
Transcribed Image Text:Table entry for C is the critical value
* required for confidence level C.
To approximate one- and two-sided
Pvalues, compare the value of the t
Tail area 15
statistic with the critical values of
Area C
that match the Pvalues given at the
bottom of the table.
TABLE C tDISTRIBUTION CRITICAL VALUES
CONFIDENCE LEVEL C
DEGREES OF
FREEDOM
50% 60% 70%
80%
90%
95%
96%
98%
99%
99.5% 99.8%
99.9%
1.000 1.376 1.963 3.078 6.314 12.71
0.816 1.061 1.386 1.886 2.920
0.765 0.978 1.250 1.638 2.353
0.741 0.941 1.190 1.533 2.132
0.727 0.920 1.156 1.476 2.015
15.89
4.849
3.482
2.999
2.757
63.66
9.925
5.841
4.604
4.032
127.3
14.09
7.453
5.598
4.773
318.3
22.33
10.21
7.173
5.893
636.6
31.60
12.92
8.610
6.869
31.82
4.303
3.182
2.776
2.571
6.965
4.541
3.747
3.365
2
000
4
5.959
3.707
3.499
3.355
3.250
3.169
5.208
4.785
4.501
4.297
4.144
4.317
0.718 0.906 1.134 1.440 1.943
0.711 0.896 1.119 1.415 1.895
0.706 0.889 1.108 1.397 1.860
0.703 0.883 1.100 1.383 1.833
0.700 0.879 1.093 1.372 1.812
2.447
2.365
2.306
2.262
2.228
2.612
2.517
2.449
2.398
2.359
3.143
2.998
2.896
2.821
2.764
6.
4.029
3.833
3.690
3.581
5.408
5.041
4.781
4.587
7.
10
0.697 0.876 1.088 1.363 1.796
0.695 0.873 1.083 1.356 1.782
0.694 0.870 1.079 1.350 1.771
0.692 0.868 1.076 1.345 1.761
0.691 0.866 1.074 1.341 1.753
2.201
2.179
2.160
2.145
2.131
2.328
2.303
2.282
2.264
2.249
2.718
2.681
2.650
2.624
2.602
3.106
3.055
3.012
2.977
2.947
3.497
3.428
3.372
3.326
3.286
4.025
3.930
3.852
3.787
3.733
4.437
4.318
4.221
4.140
4.073
11
12
13
14
15
0.690 0.865 1.071 1.337 1.746
0.689 0.863 1.069 1.333 1.740
0.688 0.862 1.067 1.330 1.734
0.688 0.861 1.066 1.328 1.729
0.687 0.860 1.064 1.325 1.725
2.120
2.110
2.101
2.093
2.086
2.235
2.224
2.214
2.205
2.197
2.583
2.567
2.552
2.539
2.528
2.921
2.898
2.878
2.861
2.845
3.252
3.222
3.197
3.174
3.153
3.686
3.646
3.611
3.579
3.552
4.015
3.965
3.922
3.883
3.850
16
17
18
19
20
3.527
3.505
3.485
3.819
21
22
23
24
25
0.686 0.859 1.063 1.323 1.721
0.686 0.858 1.061 1.321 1.717
0.685 0.858 1.060 1.319 1.714
0.685 0.857 1.059 1.318 1.711
0.684 0.856 1.058 1.316 1.708
2.080
2.074
2.069
2.064
2.060
2.189
2.183
2.177
2.172
2.167
2.518
2.508
2.500
2.492
2.485
2.831
2.819
2.807
3.135
3.119
3.104
3.792
3.768
2.797
2.787
3.091
3.078
3.467
3.450
3.745
3.725
3.067
3.057
3.047
3.038
3.030
3.707
26
27
28
29
30
0.684 0.856 1.058 1.315 1.706 2.056
2.052
2.048
2.045
2.042
1.703
0.683 0.855 1.056 1.313 1.701
1.699
1.310 1.697
2.162
2.158
2.154
2.150
2.147
2.479
2.473
2.467
2.462
2.457
2.779
2.771
2.763
2.756
2.750
3.435
3.421
3.408
3.396
3.385
3.690
3.674
3.659
3.646
0.684 0.855 1.057 1.314
0.683 0.854 1.055 1.311
0.683 0.854 1.055
2.423
2.403
2.390
2.374
2.704
2.678
2.660
2.639
2.626
2.581
2.971
2.937
2.915
2.887
2.871
2.813
3.307
3.261
3.232
3.195
3.174
3.098
3.551
3.496
3.460
3.416
3.390
3.300
2.123
2.109
2.099
40
50
60
80
100
1000
0.681 0.851 1.050 1.303 1.684
0.679 0.849 1.047 1.299 1.676
0.679 0.848 1.045 1.296 1.671
0.678 0.846
0.677 0.845 1.042 1.290 1.660
0.675 0.842 1.037 1.282 1.646
2.021
2.009
2.000
1.990
1.984
1.962
2.088
2.081
2.056
1.043 1.292
1.664
2.364
2.330
0.674 0.841 1.036 1.282 1.645
1.960
2.054
2.326
2.576
2.807
3.091
3.291
One-sided P
.25
.20
.15
.10
.05
.025
.02
„01
.005
„0025
.001
.0005
Two-sided P
50
40
30
.20
.10
.05
.04
.02
.01
„005
.002
.001
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