Study showed that the time required by workers to complete a certain task follows the normal distribution with mean of 30 mins. A group of 23 workers was chosen randomly to receive a special training for a few days. After the training, it was found that their average was 25 mins. A test of hypothesis will be conducted to determine if the special training speeds up the operation at alpha=0.05. a) state the null and alternative hypothesis in symbols b) what is the computed value c) decide whether to reject the null hypothesis or not d) give the conclusion
Study showed that the time required by workers to complete a certain task follows the normal distribution with mean of 30 mins. A group of 23 workers was chosen randomly to receive a special training for a few days. After the training, it was found that their average was 25 mins. A test of hypothesis will be conducted to determine if the special training speeds up the operation at alpha=0.05. a) state the null and alternative hypothesis in symbols b) what is the computed value c) decide whether to reject the null hypothesis or not d) give the conclusion
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
Study showed that the time required by workers to complete a certain task follows the
a) state the null and alternative hypothesis in symbols
b) what is the computed value
c) decide whether to reject the null hypothesis or not
d) give the conclusion
(The attached picture is a t-distribution table)
![Student's t Distribution Table
Forexample, the tvalue for
18 degrees of freedom
a
= 0.025
is 2.101 for 95% confidence
= 0.025
2
interval (2-Tail a = 0.05).
t value
-2
-1
1
4
90%
95%
97.5%
99%
99.5%
99.95%
1-Tail Confidence Level
80%
90%
95%
98%
99%
99.9%
2-Tail Confidence Level
0.100
0.050
0.025
0.010
0.005
0.0005
1-Tail Alpha
df
2-Tail Alpha
0.20
0.10
0.05
0.02
0.01
0.001
1
3.0777
6.3138
12.7062
31.8205
63.6567
636.6192
1.8856
2.9200
4.3027
6.9646
9.9248
31.5991
3
1.6377
2.3534
3.1824
4.5407
5.8409
12.9240
1.5332
2.1318
2.7764
3.7469
4.6041
8.6103
5
1.4759
2.0150
2.5706
3.3649
4.0321
6.8688
6
1.4398
1.9432
2.4469
3.1427
3.7074
5.9588
7
1.4149
1.8946
2.3646
2.9980
3.4995
5.4079
8
1.3968
1.8595
2.3060
2.8965
3.3554
5.0413
9
1.3830
1.8331
2.2622
2.8214
3.2498
4.7809
10
1.3722
1.8125
2.2281
2.7638
3.1693
4.5869
11
1.3634
1.7959
2.2010
2.7181
3.1058
4.4370
12
1.3562
1.7823
2.1788
2.6810
3.0545
4.3178
13
1.3502
1.7709
2.1604
2.6503
3.0123
4.2208
14
1.3450
1.7613
2.1448
2.6245
2.9768
4.1405
15
1.3406
1.7531
2.1314
2.6025
2.9467
4.0728
16
1.3368
1.7459
2.1199
2.5835
2.9208
4.0150
17
1.3334
1.7396
2.1098
2.5669
2.8982
3.9651
18
1.3304
1.7341
2.1009
2.5524
2.8784
3.9216
19
1.3277
1.7291
2.0930
2.5395
2.8609
3.8834
20
1.3253
1.7247
2.0860
2.5280
2.8453
3.8495
21
1.3232
1.7207
2.0796
2.5176
2.8314
3.8193
22
1.3212
1.7171
2.0739
2.5083
2.8188
3.7921
23
1.3195
1.7139
2.0687
2.4999
2.8073
3.7676
24
1.3178
1.7109
2.0639
2.4922
2.7969
3.7454
25
1.3163
1.7081
2.0595
2.4851
2.7874
3.7251
26
1.3150
1.7056
2.0555
2.4786
2.7787
3.7066
27
1.3137
1.7033
2.0518
2.4727
2.7707
3.6896
28
1.3125
1.7011
2.0484
2.4671
2.7633
3.6739
29
1.3114
1.6991
2.0452
2.4620
2.7564
3.6594
30
1.3104
1.6973
2.0423
2.4573
2.7500
3.6460](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd8ebdc8-eca6-4aee-b898-cf0df862412b%2F64ba8b58-8408-473f-be8d-046fcc57085d%2Fod506ls_processed.png&w=3840&q=75)
Transcribed Image Text:Student's t Distribution Table
Forexample, the tvalue for
18 degrees of freedom
a
= 0.025
is 2.101 for 95% confidence
= 0.025
2
interval (2-Tail a = 0.05).
t value
-2
-1
1
4
90%
95%
97.5%
99%
99.5%
99.95%
1-Tail Confidence Level
80%
90%
95%
98%
99%
99.9%
2-Tail Confidence Level
0.100
0.050
0.025
0.010
0.005
0.0005
1-Tail Alpha
df
2-Tail Alpha
0.20
0.10
0.05
0.02
0.01
0.001
1
3.0777
6.3138
12.7062
31.8205
63.6567
636.6192
1.8856
2.9200
4.3027
6.9646
9.9248
31.5991
3
1.6377
2.3534
3.1824
4.5407
5.8409
12.9240
1.5332
2.1318
2.7764
3.7469
4.6041
8.6103
5
1.4759
2.0150
2.5706
3.3649
4.0321
6.8688
6
1.4398
1.9432
2.4469
3.1427
3.7074
5.9588
7
1.4149
1.8946
2.3646
2.9980
3.4995
5.4079
8
1.3968
1.8595
2.3060
2.8965
3.3554
5.0413
9
1.3830
1.8331
2.2622
2.8214
3.2498
4.7809
10
1.3722
1.8125
2.2281
2.7638
3.1693
4.5869
11
1.3634
1.7959
2.2010
2.7181
3.1058
4.4370
12
1.3562
1.7823
2.1788
2.6810
3.0545
4.3178
13
1.3502
1.7709
2.1604
2.6503
3.0123
4.2208
14
1.3450
1.7613
2.1448
2.6245
2.9768
4.1405
15
1.3406
1.7531
2.1314
2.6025
2.9467
4.0728
16
1.3368
1.7459
2.1199
2.5835
2.9208
4.0150
17
1.3334
1.7396
2.1098
2.5669
2.8982
3.9651
18
1.3304
1.7341
2.1009
2.5524
2.8784
3.9216
19
1.3277
1.7291
2.0930
2.5395
2.8609
3.8834
20
1.3253
1.7247
2.0860
2.5280
2.8453
3.8495
21
1.3232
1.7207
2.0796
2.5176
2.8314
3.8193
22
1.3212
1.7171
2.0739
2.5083
2.8188
3.7921
23
1.3195
1.7139
2.0687
2.4999
2.8073
3.7676
24
1.3178
1.7109
2.0639
2.4922
2.7969
3.7454
25
1.3163
1.7081
2.0595
2.4851
2.7874
3.7251
26
1.3150
1.7056
2.0555
2.4786
2.7787
3.7066
27
1.3137
1.7033
2.0518
2.4727
2.7707
3.6896
28
1.3125
1.7011
2.0484
2.4671
2.7633
3.6739
29
1.3114
1.6991
2.0452
2.4620
2.7564
3.6594
30
1.3104
1.6973
2.0423
2.4573
2.7500
3.6460
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