To test Ho: u = 100 versus H,: µ# 100, a simple random sample size of n= 22 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). E Click here to view the t-Distribution Area in Right Tail. (a) If x = 105.1 and s= 8.3, compute the test statistic. t= (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a = 0.01 level of significance, determine the critical values. The critical values are. (Use a comma to separate answers as needed. Round to three decimal places as needed.) (c) Draw a t-distribution that depicts the critical region(s). Which of the following graphs shows the critical region(s) in the t-distribution? O A. Ов. Oc. (d) Will the researcher reject the null hypothesis? O A. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is not between the critical values. O B. The researcher will reject the null hypothesis since the test statistic is between the critical values. OC. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is between the critical values. O D. The researcher will reject the null hypothesis since the test statistic is not between the critical values.
To test Ho: u = 100 versus H,: µ# 100, a simple random sample size of n= 22 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). E Click here to view the t-Distribution Area in Right Tail. (a) If x = 105.1 and s= 8.3, compute the test statistic. t= (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a = 0.01 level of significance, determine the critical values. The critical values are. (Use a comma to separate answers as needed. Round to three decimal places as needed.) (c) Draw a t-distribution that depicts the critical region(s). Which of the following graphs shows the critical region(s) in the t-distribution? O A. Ов. Oc. (d) Will the researcher reject the null hypothesis? O A. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is not between the critical values. O B. The researcher will reject the null hypothesis since the test statistic is between the critical values. OC. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is between the critical values. O D. The researcher will reject the null hypothesis since the test statistic is not between the critical values.
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
31
Transcribed Image Text:To test Ho: µ= 100 versus H1: µ#100, a simple random sample size of n = 22 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d).
Click here to view the t-Distribution Area in Right Tail.
.....
(a) If x = 105.1 and s = 8.3, compute the test statistic.
t%D
(Round to three decimal places as needed.)
(b) If the researcher decides to test this hypothesis at the a = 0.01 level of significance, determine the critical values.
The critical values are
(Use a comma to separate answers as needed. Round to three decimal places as needed.)
(c) Draw a t-distribution that depicts the critical region(s). Which of the following graphs shows the critical region(s) in the t-distribution?
A.
В.
C.
(d) Will the researcher reject the null hypothesis?
O A. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is not between the critical values.
B. The researcher will reject the null hypothesis since the test statistic is between the critical values.
C. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is between the critical values.
D. The researcher will reject the null hypothesis since the test statistic is not between the critical values.
Transcribed Image Text:t-Distribution
Arca
Right Tail
df
0.25
0,20
0.15
0.10
0.05
0,025
0,02
(0,01
0.005
0.0025
0,001
0,0005
df
63.657
9.925
5.841
4.604
4.032
318.309
22.327
10.215
7.173
5.893
3.078
1.886
15.894
4.849
3.482
2.999
2.757
127.321
14.089
7.453
5.598
4.773
636.619
31.599
12.924
8.610
6.869
1
1.000
1.376
1.963
6.314
2.920
2.353
2.132
2.015
12.706
31.821
6.965
4.541
3.747
3.365
1
4.303
3.182
2.776
2.571
0.816
3
1.061
0.978
0.941
0.920
1.386
1.250
1.190
2
0.765
0.741
0.727
1.638
1.533
1.476
3
1.156
0.718
0.711
8
0.906
0.896
0.889
0.883
0.879
1.134
1.119
1.108
1.100
1.093
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
2.612
2.517
2.449
2.398
2.359
3.143
2.998
2.896
2.821
2.764
3.707
3.499
3.355
3.250
3.169
4.317
4.029
3.833
3.690
3.581
5.208
4.785
4.501
4.297
4.144
5.959
5.408
5.041
4.781
4.587
6.
6
0.706
0.703
8
2.262
2.228
10
0.700
10
1.088
1.083
1.079
1.363
1.356
1.350
1.345
1.341
2.201
2.179
2.160
2.145
2.131
0.876
4.025
3.930
3.852
3.787
3.733
11
0.697
1.796
2.328
2.303
2.282
2.264
2.249
2.718
3.106
3.497
3.428
4.437
11
1.782
1.771
1.761
1.753
3.055
3.012
2.977
12
0.695
0.873
0.870
0.868
0.866
2.681
2.650
2.624
2.602
4.318
4.221
4.140
4.073
12
13
3.372
3.326
3.286
0.694
13
0.692
0.691
14
1.076
14
15
1.074
2.947
15
0,865
0.863
0.862
0.861
0.860
1.337
1.333
1.330
1.328
1.325
3.252
3.222
3.197
3.174
3.153
0.690
0.689
1.071
1.069
1.067
1.066
1.064
1.746
1.740
1.734
1.729
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
16
17
3.686
3.646
4.015
3.965
16
17
18
0.688
3.610
3.922
3.883
3.850
18
0.688
3.579
3.552
19
20
19
20
0,687
0.686
0,686
0.685
0.685
0.684
0.859
0,858
0,858
0857
0.856
1.063
1.061
1.060
1.059
1.058
1.323
1.321
1.319
1.318
1.316
3.819
3.792
3.768
3.745
3.725
2.831
2.819
1.721
1.717
1.714
1.711
1.708
3.527
3.505
3.485
3.467
3.450
21
22
2.080
2.074
3.135
3.119
2.189
2.183
2.177
2.172
2.167
2.518
2.508
2.500
2.492
2.485
21
22
2.069
2.064
2.060
2,807
2.797
3.104
3.091
3.078
23
23
24
24
25
2.787
25
1.058
1.057
0.684
0,684
0.683
0.856
0,855
0,855
0,854
0.854
2.479
2.473
2.467
2.462
2.457
3.707
3.690
3.674
3.659
3.646
3.435
3.421
2.056
2.052
2.048
2.045
2.042
3.067
3.057
3.047
3.038
3.030
26
27
1.315
1.314
1.313
1.311
1.310
1.706
1.703
1.701
1.699
1.697
2.162
2.158
2.154
2.150
2.147
2.779
2.771
2.763
2.756
2.750
26
27
28
1.056
3.408
28
29
30
0,683
0.683
1.055
1.055
3.396
3.385
29
30
0,853
0.853
0,853
0.852
0.852
2.040
2.037
2.035
2.032
2.030
2.144
2.141
2.138
2.136
2.133
2.453
2.449
2.445
2.744
2.738
2.733
2.728
2.724
3.022
3.015
3.008
3.002
2.996
3.375
3.365
3.356
3.348
3.340
3.633
3.622
3.611
3.601
3.591
31
0.682
0.682
0.682
0.682
0.682
1.054
1.309
1.696
31
1.054
1.053
1.052
1.052
1.309
1.308
32
1.694
1.692
1.691
1.690
32
33
33
34
35
1.307
1.306
2.441
34
35
2.438
0.681
0.681
0.681
0.681
1.688
1.687
1.686
1.685
1.684
2.028
2.026
2.024
2.023
2.021
2.131
2.129
2.127
2.125
2.123
2.990
2.985
2.980
2.976
2.971
3.333
3.326
3.319
3.313
3.307
0,852
2.719
2.715
2.712
2.708
2.704
3.582
3.574
3.566
3.558
3.551
36
1.052
1.051
1.051
1.050
1.306
1.305
1.304
1.304
1.303
2.434
2.431
2.429
2.426
2.423
36
37
0.851
0.851
0.851
0.851
37
38
39
38
39
40
0.681
1.050
40
2.937
2.915
2.009
2.000
1.994
1.990
2.678
2.660
2.648
2.639
2.632
3.261
3.232
3.211
3.195
3.183
3.496
3.460
3.435
3.416
3.402
50
0.679
0.849
1.047
1.299
1.676
2.109
2.403
50
0.679
0,678
0,678
0.677
0,848
0.847
0.846
0.846
1.045
1.044
1.043
1.042
1.296
1.294
1.292
1.291
1.671
1.667
1.664
1.662
2.099
2.093
2.088
2.084
2.390
2.381
2.374
60
60
70
80
2.899
2.887
2.878
70
80
90
1.987
2.368
90
0.677
0.675
0,674
1.042
1.037
1.036
1.660
1.646
1.645
1.984
1.962
1.960
2.364
2.330
2.326
100
0,845
0.842
0,842
1.290
1.282
1.282
2.081
2.056
2.054
2.626
2.581
2.576
2.871
2.813
2.807
3.174
3.098
3.090
3.390
3.300 1000
3.291 z
100
1000
df
0.25
0,20
0,15
0.10
0,05
0.025
0,.02
0.01
0.005
0.0025
0.001
0.0005
df
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