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 with a standard deviation of 3 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 symbolsb) what is the computed valuec) decide whether to reject the null hypothesis or notd) give the conclusion Student's t Distribution TableForexample, the tvalue for18 degrees of freedoma= 0.025is 2.101 for 95% confidence= 0.0252interval (2-Tail a = 0.05).t value-2-11490%95%97.5%99%99.5%99.95%1-Tail Confidence Level80%90%95%98%99%99.9%2-Tail Confidence Level0.1000.0500.0250.0100.0050.00051-Tail Alphadf2-Tail Alpha0.200.100.050.020.010.00113.07776.313812.706231.820563.6567636.61921.88562.92004.30276.96469.924831.599131.63772.35343.18244.54075.840912.92401.53322.13182.77643.74694.60418.610351.47592.01502.57063.36494.03216.868861.43981.94322.44693.14273.70745.958871.41491.89462.36462.99803.49955.407981.39681.85952.30602.89653.35545.041391.38301.83312.26222.82143.24984.7809101.37221.81252.22812.76383.16934.5869111.36341.79592.20102.71813.10584.4370121.35621.78232.17882.68103.05454.3178131.35021.77092.16042.65033.01234.2208141.34501.76132.14482.62452.97684.1405151.34061.75312.13142.60252.94674.0728161.33681.74592.11992.58352.92084.0150171.33341.73962.10982.56692.89823.9651181.33041.73412.10092.55242.87843.9216191.32771.72912.09302.53952.86093.8834201.32531.72472.08602.52802.84533.8495211.32321.72072.07962.51762.83143.8193221.32121.71712.07392.50832.81883.7921231.31951.71392.06872.49992.80733.7676241.31781.71092.06392.49222.79693.7454251.31631.70812.05952.48512.78743.7251261.31501.70562.05552.47862.77873.7066271.31371.70332.05182.47272.77073.6896281.31251.70112.04842.46712.76333.6739291.31141.69912.04522.46202.75643.6594301.31041.69732.04232.45732.75003.6460

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Description: 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 t

Here, a t-test will be used. Population mean, μ=30 Sample mean, x=25 Sample size, n=25 Sample sd,…

Answered: Study showed that the time required by…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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 with a standard deviation of 3 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

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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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