- TABLES 701 Table entry for C is the critical value * required for confidence level C. To approximate one- and two-sided P-values, compare the value of the t statistic with the critical values of t" Tail area 15 Area C that match the P-values given at the bottom of the table. TABLEC t DISTRIBUTION CRITICAL VALUES CONFIDENCE LEVEL C DEGREES OF FREEDOM 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% 636.6 63.66 9.925 127.3 14.09 7.453 5.598 318.3 31.82 6.965 1.963 1.386 1.250 1.190 1.156 6.314 2.920 2.353 2.132 12.71 4.303 3.182 2.776 2.571 15.89 4.849 3.482 2.999 3.078 1.000 1.376 0.816 1.061 0.978 0.765 0.741 0.941 0.727 0.920 1 31.60 12.92 1.886 22.33 4.541 3.747 5.841 4.604 4.032 10.21 7.173 5.893 1.638 00.05 8.610 1.533 1.476 4 ILS 5 2.015 2.757 3.365 4.773 6.869 5.208 4.785 4.501 4.297 4.144 5.959 4.317 4.029 2.612 2.517 2.449 2.398 2.359 3.707 3.499 3.355 3.250 3.143 2.998 0.718 0.906 0.896 0.889 0.883 0.879 1.440 1.415 1.397 1.383 1.372 1.943 1.895 1.860 1.833 1.812 2.447 2.365 2.306 2.262 2.228 6. 1.134 5.408 5.041 4.781 4.587 7 0.711 1.119 2.896 2.821 2.764 3.833 8. 9. 0.706 0.703 0.700 1.108 1.100 3.690 3.581 10 1.093 3.169 2.718 2.681 2.650 2.624 3.106 3.055 3.012 2.977 2.947 3.497 3.428 3.372 4.025 3.930 3.852 3.787 3.733 4.437 4.318 4.221 4.140 1.363 1.356 1.796 1.782 2.201 2.179 2.160 2.145 2.328 0.697 0.876 0.695 0.873 0.694 0.692 0.868 1.076 1.345 0.691 11 1.088 12 1.083 2.303 2.282 2.264 2.249 13 0.870 1.079 1.350 1.771 14 1.761 3.326 15 0.866 1.074 1.341 1.753 2.131 2.602 3.286 4.073 4.015 3.965 3.922 3.883 3.850 3.252 3.222 3.686 3.646 3.611 3.579 2.921 2.898 1.746 1.740 1.734 2.235 2.224 2.214 2.583 2.567 2.552 2.539 2.528 2.120 0.865 1.071 1.069 1.067 1.066 1.064 1.337 0.690 0.689 16 2.110 0.863 0.862 17 1.333 2.878 2.861 2.845 18 0.688 1.330 2.101 3.197 2.093 2.086 3.174 3.153 2.205 1.328 1.325 1.729 1.725 19 0.688 0.861 20 0.687 0.860 2.197 3.552 3.527 3.505 3.485 3.467 3.450 3.819 3.792 3.768 3.745 3.725 3.135 2.189 2.183 2.518 2.508 2.500 2.492 2.485 2.831 1.323 1.321 1.319 1.721 1.717 1.714 1.711 1.708 2.080 2.074 2.069 2.064 0.686 0.859 0.858 0.686 1.063 1.061 2.819 3.119 22 GO.S23 3.104 1.060 1.059 1.058 2.177 2.172 2.167 2.807 2.797 2.787 0.685 0.858 1.318 3.091 0.685 0.857 0.684 0.856 24 25 1.316 2.060 3.078 3.435 3.421 3.408 3.396 3.385 2.779 3.067 3.707 1.706 1.703 1.701 1.699 1.697 2.162 2.158 2.154 2.150 2.479 2.473 2.467 2.462 2.457 1.058 1.057 1.315 1.314 1.313 2.056 0.684 0.684 0.683 0.856 0.855 26 3.690 3.057 3.047 2.771 2.052 2.048 2.045 2.042 27 2.763 2.756 3.674 3.659 3.646 28 0.855 1.056 1.311 3.038 0.854 0.854 1.055 29 30 0.683 0.683 1.055 1.310 2.147 2.750 3.030 3.551 2.971 2.937 3.307 3.261 1.050 1.047 1.299 0.679 0.848 1.045 1.296 0.846 1.043 1.292 1.042 1.290 1.037 1.684 1.676 1.671 1.664 1.660 1.646 2.123 2.109 2.099 2.088 2.081 2.056 2.423 2.403 2.390 2.374 2.364 2.330 2.704 2.678 2.660 2.639 2.626 1.303 2.021 0.681 0.679 0.851 40 50 60 80 100 1000 2.009 2.000 1.990 3.496 3.460 0.849 2.915 3.232 2.887 2.871 2.813 0.678 3.195 3.416 3.390 3.300 1.984 3.174 0.677 0.845 0.675 0.842 1.282 1.962 2.581 3.098 0.674 0.841 1.036 1.282 1.645 1.960 2.054 2.326 2.576 2.807 3.0 3.291 One-sided P .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .0005 Two-sided P .50 .40 .30 .20 .10 .05 .04 .02 .01 .005 .002 .001 We randomly select 10 individuals from a large group who has participated in an SAT-Math tutorial. We would like to find out if there is good evidence that the tutorial improves average scores on the SAT-M test. Each individual's baseline score and score after the tutorial is recorded below (along with the difference between the baseline and the after tutorial test). We can assume that the distribution of difference is relatively normal. Individual # SAT-M Baseline SAT-M (after tutorial) Difference 1 680 690 10 540 560 20 3 590 600 10 4 620 620 630 600 -30 660 670 10 7 490 500 10 8 510 500 -10 9 700 710 10 10 420 443 23 The average difference from the sample is 5.3 and the sample standard deviation is 15.4 A researcher hopes to find evidence that the tutorial increases overall SAT-M scores. 1. What are the null and alternative hypothesis statements for this problem? 2. Using the equation below, calculate the resulting t-statistic (show your work and/or describe the process) X - 0 t = 8/Nn 3. Report the degrees of freedom and the critical value for an alpha level of .05 (see table below) 4. Can we reject the null hypothesis? Why or why not?
- TABLES 701 Table entry for C is the critical value * required for confidence level C. To approximate one- and two-sided P-values, compare the value of the t statistic with the critical values of t" Tail area 15 Area C that match the P-values given at the bottom of the table. TABLEC t DISTRIBUTION CRITICAL VALUES CONFIDENCE LEVEL C DEGREES OF FREEDOM 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% 636.6 63.66 9.925 127.3 14.09 7.453 5.598 318.3 31.82 6.965 1.963 1.386 1.250 1.190 1.156 6.314 2.920 2.353 2.132 12.71 4.303 3.182 2.776 2.571 15.89 4.849 3.482 2.999 3.078 1.000 1.376 0.816 1.061 0.978 0.765 0.741 0.941 0.727 0.920 1 31.60 12.92 1.886 22.33 4.541 3.747 5.841 4.604 4.032 10.21 7.173 5.893 1.638 00.05 8.610 1.533 1.476 4 ILS 5 2.015 2.757 3.365 4.773 6.869 5.208 4.785 4.501 4.297 4.144 5.959 4.317 4.029 2.612 2.517 2.449 2.398 2.359 3.707 3.499 3.355 3.250 3.143 2.998 0.718 0.906 0.896 0.889 0.883 0.879 1.440 1.415 1.397 1.383 1.372 1.943 1.895 1.860 1.833 1.812 2.447 2.365 2.306 2.262 2.228 6. 1.134 5.408 5.041 4.781 4.587 7 0.711 1.119 2.896 2.821 2.764 3.833 8. 9. 0.706 0.703 0.700 1.108 1.100 3.690 3.581 10 1.093 3.169 2.718 2.681 2.650 2.624 3.106 3.055 3.012 2.977 2.947 3.497 3.428 3.372 4.025 3.930 3.852 3.787 3.733 4.437 4.318 4.221 4.140 1.363 1.356 1.796 1.782 2.201 2.179 2.160 2.145 2.328 0.697 0.876 0.695 0.873 0.694 0.692 0.868 1.076 1.345 0.691 11 1.088 12 1.083 2.303 2.282 2.264 2.249 13 0.870 1.079 1.350 1.771 14 1.761 3.326 15 0.866 1.074 1.341 1.753 2.131 2.602 3.286 4.073 4.015 3.965 3.922 3.883 3.850 3.252 3.222 3.686 3.646 3.611 3.579 2.921 2.898 1.746 1.740 1.734 2.235 2.224 2.214 2.583 2.567 2.552 2.539 2.528 2.120 0.865 1.071 1.069 1.067 1.066 1.064 1.337 0.690 0.689 16 2.110 0.863 0.862 17 1.333 2.878 2.861 2.845 18 0.688 1.330 2.101 3.197 2.093 2.086 3.174 3.153 2.205 1.328 1.325 1.729 1.725 19 0.688 0.861 20 0.687 0.860 2.197 3.552 3.527 3.505 3.485 3.467 3.450 3.819 3.792 3.768 3.745 3.725 3.135 2.189 2.183 2.518 2.508 2.500 2.492 2.485 2.831 1.323 1.321 1.319 1.721 1.717 1.714 1.711 1.708 2.080 2.074 2.069 2.064 0.686 0.859 0.858 0.686 1.063 1.061 2.819 3.119 22 GO.S23 3.104 1.060 1.059 1.058 2.177 2.172 2.167 2.807 2.797 2.787 0.685 0.858 1.318 3.091 0.685 0.857 0.684 0.856 24 25 1.316 2.060 3.078 3.435 3.421 3.408 3.396 3.385 2.779 3.067 3.707 1.706 1.703 1.701 1.699 1.697 2.162 2.158 2.154 2.150 2.479 2.473 2.467 2.462 2.457 1.058 1.057 1.315 1.314 1.313 2.056 0.684 0.684 0.683 0.856 0.855 26 3.690 3.057 3.047 2.771 2.052 2.048 2.045 2.042 27 2.763 2.756 3.674 3.659 3.646 28 0.855 1.056 1.311 3.038 0.854 0.854 1.055 29 30 0.683 0.683 1.055 1.310 2.147 2.750 3.030 3.551 2.971 2.937 3.307 3.261 1.050 1.047 1.299 0.679 0.848 1.045 1.296 0.846 1.043 1.292 1.042 1.290 1.037 1.684 1.676 1.671 1.664 1.660 1.646 2.123 2.109 2.099 2.088 2.081 2.056 2.423 2.403 2.390 2.374 2.364 2.330 2.704 2.678 2.660 2.639 2.626 1.303 2.021 0.681 0.679 0.851 40 50 60 80 100 1000 2.009 2.000 1.990 3.496 3.460 0.849 2.915 3.232 2.887 2.871 2.813 0.678 3.195 3.416 3.390 3.300 1.984 3.174 0.677 0.845 0.675 0.842 1.282 1.962 2.581 3.098 0.674 0.841 1.036 1.282 1.645 1.960 2.054 2.326 2.576 2.807 3.0 3.291 One-sided P .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .0005 Two-sided P .50 .40 .30 .20 .10 .05 .04 .02 .01 .005 .002 .001 We randomly select 10 individuals from a large group who has participated in an SAT-Math tutorial. We would like to find out if there is good evidence that the tutorial improves average scores on the SAT-M test. Each individual's baseline score and score after the tutorial is recorded below (along with the difference between the baseline and the after tutorial test). We can assume that the distribution of difference is relatively normal. Individual # SAT-M Baseline SAT-M (after tutorial) Difference 1 680 690 10 540 560 20 3 590 600 10 4 620 620 630 600 -30 660 670 10 7 490 500 10 8 510 500 -10 9 700 710 10 10 420 443 23 The average difference from the sample is 5.3 and the sample standard deviation is 15.4 A researcher hopes to find evidence that the tutorial increases overall SAT-M scores. 1. What are the null and alternative hypothesis statements for this problem? 2. Using the equation below, calculate the resulting t-statistic (show your work and/or describe the process) X - 0 t = 8/Nn 3. Report the degrees of freedom and the critical value for an alpha level of .05 (see table below) 4. Can we reject the null hypothesis? Why or why not?
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
Transcribed Image Text:- TABLES
701
Table entry for C is the critical value
* required for confidence level C.
To approximate one- and two-sided
P-values, compare the value of the t
statistic with the critical values of t"
Tail area 15
Area C
that match the P-values given at the
bottom of the table.
TABLEC
t DISTRIBUTION CRITICAL VALUES
CONFIDENCE LEVEL C
DEGREES OF
FREEDOM
50%
60%
70%
80%
90%
95%
96%
98%
99%
99.5%
99.8%
99.9%
636.6
63.66
9.925
127.3
14.09
7.453
5.598
318.3
31.82
6.965
1.963
1.386
1.250
1.190
1.156
6.314
2.920
2.353
2.132
12.71
4.303
3.182
2.776
2.571
15.89
4.849
3.482
2.999
3.078
1.000
1.376
0.816
1.061
0.978
0.765
0.741
0.941
0.727 0.920
1
31.60
12.92
1.886
22.33
4.541
3.747
5.841
4.604
4.032
10.21
7.173
5.893
1.638
00.05
8.610
1.533
1.476
4
ILS 5
2.015
2.757
3.365
4.773
6.869
5.208
4.785
4.501
4.297
4.144
5.959
4.317
4.029
2.612
2.517
2.449
2.398
2.359
3.707
3.499
3.355
3.250
3.143
2.998
0.718 0.906
0.896
0.889
0.883
0.879
1.440
1.415
1.397
1.383
1.372
1.943
1.895
1.860
1.833
1.812
2.447
2.365
2.306
2.262
2.228
6.
1.134
5.408
5.041
4.781
4.587
7
0.711
1.119
2.896
2.821
2.764
3.833
8.
9.
0.706
0.703
0.700
1.108
1.100
3.690
3.581
10
1.093
3.169
2.718
2.681
2.650
2.624
3.106
3.055
3.012
2.977
2.947
3.497
3.428
3.372
4.025
3.930
3.852
3.787
3.733
4.437
4.318
4.221
4.140
1.363
1.356
1.796
1.782
2.201
2.179
2.160
2.145
2.328
0.697 0.876
0.695 0.873
0.694
0.692 0.868 1.076 1.345
0.691
11
1.088
12
1.083
2.303
2.282
2.264
2.249
13
0.870 1.079
1.350
1.771
14
1.761
3.326
15
0.866 1.074
1.341
1.753
2.131
2.602
3.286
4.073
4.015
3.965
3.922
3.883
3.850
3.252
3.222
3.686
3.646
3.611
3.579
2.921
2.898
1.746
1.740
1.734
2.235
2.224
2.214
2.583
2.567
2.552
2.539
2.528
2.120
0.865 1.071
1.069
1.067
1.066
1.064
1.337
0.690
0.689
16
2.110
0.863
0.862
17
1.333
2.878
2.861
2.845
18
0.688
1.330
2.101
3.197
2.093
2.086
3.174
3.153
2.205
1.328
1.325
1.729
1.725
19
0.688
0.861
20
0.687
0.860
2.197
3.552
3.527
3.505
3.485
3.467
3.450
3.819
3.792
3.768
3.745
3.725
3.135
2.189
2.183
2.518
2.508
2.500
2.492
2.485
2.831
1.323
1.321
1.319
1.721
1.717
1.714
1.711
1.708
2.080
2.074
2.069
2.064
0.686 0.859
0.858
0.686
1.063
1.061
2.819
3.119
22
GO.S23
3.104
1.060
1.059
1.058
2.177
2.172
2.167
2.807
2.797
2.787
0.685
0.858
1.318
3.091
0.685 0.857
0.684 0.856
24
25
1.316
2.060
3.078
3.435
3.421
3.408
3.396
3.385
2.779
3.067
3.707
1.706
1.703
1.701
1.699
1.697
2.162
2.158
2.154
2.150
2.479
2.473
2.467
2.462
2.457
1.058
1.057
1.315
1.314
1.313
2.056
0.684
0.684
0.683
0.856
0.855
26
3.690
3.057
3.047
2.771
2.052
2.048
2.045
2.042
27
2.763
2.756
3.674
3.659
3.646
28
0.855
1.056
1.311
3.038
0.854
0.854
1.055
29
30
0.683
0.683
1.055
1.310
2.147
2.750
3.030
3.551
2.971
2.937
3.307
3.261
1.050
1.047 1.299
0.679 0.848 1.045 1.296
0.846 1.043 1.292
1.042 1.290
1.037
1.684
1.676
1.671
1.664
1.660
1.646
2.123
2.109
2.099
2.088
2.081
2.056
2.423
2.403
2.390
2.374
2.364
2.330
2.704
2.678
2.660
2.639
2.626
1.303
2.021
0.681
0.679
0.851
40
50
60
80
100
1000
2.009
2.000
1.990
3.496
3.460
0.849
2.915
3.232
2.887
2.871
2.813
0.678
3.195
3.416
3.390
3.300
1.984
3.174
0.677 0.845
0.675
0.842
1.282
1.962
2.581
3.098
0.674
0.841
1.036
1.282 1.645
1.960
2.054
2.326
2.576
2.807
3.0
3.291
One-sided P
.25
.20
.15
.10
.05
.025
.02
.01
.005
.0025
.0005
Two-sided P
.50
.40
.30
.20
.10
.05
.04
.02
.01
.005
.002
.001
Transcribed Image Text:We randomly select 10 individuals from a large group who has participated in an SAT-Math
tutorial. We would like to find out if there is good evidence that the tutorial improves
average scores on the SAT-M test. Each individual's baseline score and score after the
tutorial is recorded below (along with the difference between the baseline and the after
tutorial test). We can assume that the distribution of difference is relatively normal.
Individual #
SAT-M Baseline
SAT-M (after tutorial) Difference
1
680
690
10
540
560
20
3
590
600
10
4
620
620
630
600
-30
660
670
10
7
490
500
10
8
510
500
-10
9
700
710
10
10
420
443
23
The average difference from the sample is 5.3 and the sample standard deviation is
15.4
A researcher hopes to find evidence that the tutorial increases overall SAT-M scores.
1. What are the null and alternative hypothesis statements for this problem?
2. Using the equation below, calculate the resulting t-statistic (show your work and/or
describe the process)
X - 0
t =
8/Nn
3. Report the degrees of freedom and the critical value for an alpha level of .05 (see table
below)
4. Can we reject the null hypothesis? Why or why not?
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