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 symbolsb) what is the computed valuec) decide whether to reject the null hypothesis or notd) give the conclusion(The attached picture is a t-distribution table) 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

Given data is appropriate for testing of hypothesis to test for t-test for single mean . because it…

Answered: Study showed that the time required by…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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. 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

(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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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