-Suppose we fail to reject Ho: μ ≥ 50 When the true mean is μ = 53Given a sample of size n=64 and σ =6 and with α=0.05Calculate the critical sample mean Xα , the ZX̅α , The probability of type II error βand the power of the hypothesis test P.Solution: [Write the rules/formula]Calculate X̅α :Calculate ZX̅α with the true mean μ = 53:The probability of type II error β:The power of the hypothesis test P: Table-1: Positive z-tableNNNNNNNNNNŇ Š Š Š Šm23456789012348849 88697734 77649505 95159931 993299619854Table-3: Negative z-table000100000700005.0000334090 3372423576 2327020611 2032717879 1761915625 153000000200240 .0023300175 0016900120 NOT00064 000620004500043.00032.00031 .00030.00022.00022 0002100015 .00015 .000140000700003 .0000300006000030.0532636 3227019766 1948917106 168531445714917 .1468600006000040000313190118943.16354.14007.00025.000170000500003.000020000300002 Table-5: t-Table One TaleDF0023........4567891011121314151617181920212223* * * * * * * * * *1000A = 0.1ta - 1.2823.0781.8861.6381.5331.4761-441.4151.3971.3831.372Baye1.3631.3031.3561.351.345Tom1.341comm1.3371.3331.331.3281.3251.3231.3211.3191.3181.3161.3151.3141.3131.3111.311.2961.2891.2820.051.6456.3142.922.3532.1322.0151.9431.8951.861.8331.8121.7961.7821.7711.7611.75310161.7461.741.7341.7291.725P1.7211.717B17141.711com1.7081.7061.7031.7011.6991.6971.6711.6581.6460.0251.9612.7064.3033.1822.776B2.5712.4472.3652.3062.2622.2282.2012:2012.1792.162.1452.1310.102.122.112.1012.0932.0862.082.0742.0692.0640.062.062.0562.0522.0482.0452.04221.981.9620.012.32631.8216.9654-5413-7473.3653.1432.9982,8962.8212.7642:7092.7182:7182.6812.652.6242.6022.5832.5672.5522.5392.5282.5182.5082.52.4922.4852.4792.4732.4672.4622-4572.392.3582.330.0052.57663.6569.9255.8414.6044.0323.7073-4993-3553.253.1693.1063.1003.0553.0122.om2.9772.9472.921...2.898..2.8782.8612.8452.8312.8192.8072.7972.7872.7792.7712.7632.7562.752.662.6172.5810.0013.091318.28922.32810.2147.1735.8945.2084-7854-5014.2974.144400944.0254:0253.933.85297873-7873.7333.6863.6462613.613-5793-5523-5273-5053-4853.4673-453-4353-4213.4083.3963.3853.2323.163.0980.00053.291636.57831.612.9248.616.8695-9595-4085.0414.7814-5874-4374-4374-3184:221.....4-144.073com4.0153.9653.9223.8833.853.8193-7923.7683.745..3.7253.7073.6893.6743.663.6463-463-3733-3Table-5: t-Table Two TailDF23456789101112131415161718192021222324252627282930601208A = 0.2ta - 1.2823.0781.8861.6381.5331.4761.4151.3971.3831.3721.3631.3561.351.3451.3411:3411.3371.3331001.3310081.328Loor1.3251.3231.3211.3191.3181.3161.2151.3151011.3141.3131.3111.311.2961.2891.2820.11.6456.3142.922.2592-3532 1922.1322.0151.9431.8951.861.8331.8121.7961.7821.7711.7611.7531:7531.7461.7417241.7341.7291.725...1.7211.7171.7141.7111.7081.70617091.7031.7011.6991.6971.6711.6581.6450.051.96t12.7064.3033.1822.7762.5712.4472.3652.3062.2622.2282.2012.1792.162.145B2.131ange2.122.112:112.1012.0932.0862.002.082.0742.0692.0642.062.05620522.05220182.0482.0452.04221.981.960.022.32631.8216.9654-5413-7473.3653.1432.9982.8962.8212.7642.7182.6812.652.6242.6022.5832.5672.5522.5392.5282.5182.5082.52.4922.4852.4702-4792.4732.4672.4622-4572.392.3582.3260.012.57663.6569.9255.841+6014.6044.0323.707Ba3-4993.3553.253.1693.1063.0553.0122.977com2.9472.9212.8982.8782.86108.2.8452.8312.8192.8072.7972.7872002.779Am2.771anta2.7632.7562.752.662.6172.5760.0023.091318.28922.32810.2147.1735.894....M5.2084-7854-5014.2974.1444.0253.933.8523-787syy3.7333.6863.6463.613-5793-5523-5273-5053.4853.4673.453.452.4253-43504013-4213-4083.3963.3853.2323.163.0910.0013.291636.57831.612.9248.6160606.869..com5.9595-4085.041B4.7814-5874-4374-3184.2214-144.0734.0153.9653.9223.883a sc3.850 8103.8193-7923.7683.7453.7253-7072 6803.6893.6742.663.663.6463-463-3733.291

It is hypothesized that: H0:μ≥50 against H1:μ<50. It is specified that:σ=6, n=64. And the desired…

Answered: Suppose we fail to reject Ho: μ ≥ 50…

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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Related questions

Question

-Suppose we fail to reject Ho: μ ≥ 50 When the true mean is μ = 53
Given a sample of size n=64 and σ =6 and with α=0.05
Calculate the critical sample mean Xα , the ZX̅α , The probability of type II error β
and the power of the hypothesis test P.
Solution: [Write the rules/formula]
Calculate X̅α :
Calculate ZX̅α with the true mean μ = 53:
The probability of type II error β:
The power of the hypothesis test P:

Table-1: Positive z-table
NNNNNNNNNNŇ Š Š Š Šm
2345678901234
8849 8869
7734 7764
9505 9515
9931 9932
9961
9854
Table-3: Negative z-table
00010
00007
00005
.00003
34090 33724
23576 23270
20611 20327
17879 17619
15625 15300
00002
00240 .00233
00175 00169
00120 NOT
00064 00062
00045
00043
.00032
.00031 .00030
.00022
.00022 00021
00015 .00015 .00014
00007
00003 .00003
00006
00003
0.05
32636 32270
19766 19489
17106 16853
14457
14917 .14686
00006
00004
00003
131901
18943
.16354
.14007
.00025
.00017
00005
00003
.00002
00003
00002

Table-5: t-Table One Tale
DF
00
2
3
........
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
* * * * * * * * * *
1000
A = 0.1
ta - 1.282
3.078
1.886
1.638
1.533
1.476
1-44
1.415
1.397
1.383
1.372
Baye
1.363
1.303
1.356
1.35
1.345
Tom
1.341
comm
1.337
1.333
1.33
1.328
1.325
1.323
1.321
1.319
1.318
1.316
1.315
1.314
1.313
1.311
1.31
1.296
1.289
1.282
0.05
1.645
6.314
2.92
2.353
2.132
2.015
1.943
1.895
1.86
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1016
1.746
1.74
1.734
1.729
1.725
P
1.721
1.717
B
1714
1.711
com
1.708
1.706
1.703
1.701
1.699
1.697
1.671
1.658
1.646
0.025
1.96
12.706
4.303
3.182
2.776
B
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2:201
2.179
2.16
2.145
2.131
0.10
2.12
2.11
2.101
2.093
2.086
2.08
2.074
2.069
2.064
0.06
2.06
2.056
2.052
2.048
2.045
2.042
2
1.98
1.962
0.01
2.326
31.821
6.965
4-541
3-747
3.365
3.143
2.998
2,896
2.821
2.764
2:709
2.718
2:718
2.681
2.65
2.624
2.602
2.583
2.567
2.552
2.539
2.528
2.518
2.508
2.5
2.492
2.485
2.479
2.473
2.467
2.462
2-457
2.39
2.358
2.33
0.005
2.576
63.656
9.925
5.841
4.604
4.032
3.707
3-499
3-355
3.25
3.169
3.106
3.100
3.055
3.012
2.om
2.977
2.947
2.921
...
2.898
..
2.878
2.861
2.845
2.831
2.819
2.807
2.797
2.787
2.779
2.771
2.763
2.756
2.75
2.66
2.617
2.581
0.001
3.091
318.289
22.328
10.214
7.173
5.894
5.208
4-785
4-501
4.297
4.144
40094
4.025
4:025
3.93
3.852
9787
3-787
3.733
3.686
3.646
261
3.61
3-579
3-552
3-527
3-505
3-485
3.467
3-45
3-435
3-421
3.408
3.396
3.385
3.232
3.16
3.098
0.0005
3.291
636.578
31.6
12.924
8.61
6.869
5-959
5-408
5.041
4.781
4-587
4-437
4-437
4-318
4:221
.....
4-14
4.073
com
4.015
3.965
3.922
3.883
3.85
3.819
3-792
3.768
3.745
..
3.725
3.707
3.689
3.674
3.66
3.646
3-46
3-373
3-3
Table-5: t-Table Two Tail
DF
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
60
120
8
A = 0.2
ta - 1.282
3.078
1.886
1.638
1.533
1.476
1.415
1.397
1.383
1.372
1.363
1.356
1.35
1.345
1.341
1:341
1.337
1.333
100
1.33
1008
1.328
Loor
1.325
1.323
1.321
1.319
1.318
1.316
1.215
1.315
101
1.314
1.313
1.311
1.31
1.296
1.289
1.282
0.1
1.645
6.314
2.92
2.259
2-353
2 192
2.132
2.015
1.943
1.895
1.86
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1:753
1.746
1.74
1724
1.734
1.729
1.725
...
1.721
1.717
1.714
1.711
1.708
1.706
1709
1.703
1.701
1.699
1.697
1.671
1.658
1.645
0.05
1.96
t
12.706
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.16
2.145
B
2.131
ange
2.12
2.11
2:11
2.101
2.093
2.086
2.00
2.08
2.074
2.069
2.064
2.06
2.056
2052
2.052
2018
2.048
2.045
2.042
2
1.98
1.96
0.02
2.326
31.821
6.965
4-541
3-747
3.365
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.65
2.624
2.602
2.583
2.567
2.552
2.539
2.528
2.518
2.508
2.5
2.492
2.485
2.470
2-479
2.473
2.467
2.462
2-457
2.39
2.358
2.326
0.01
2.576
63.656
9.925
5.841
+601
4.604
4.032
3.707
Ba
3-499
3.355
3.25
3.169
3.106
3.055
3.012
2.977
com
2.947
2.921
2.898
2.878
2.861
08.
2.845
2.831
2.819
2.807
2.797
2.787
200
2.779
Am
2.771
anta
2.763
2.756
2.75
2.66
2.617
2.576
0.002
3.091
318.289
22.328
10.214
7.173
5.894
....
M
5.208
4-785
4-501
4.297
4.144
4.025
3.93
3.852
3-787
syy
3.733
3.686
3.646
3.61
3-579
3-552
3-527
3-505
3.485
3.467
3.45
3.45
2.425
3-435
0401
3-421
3-408
3.396
3.385
3.232
3.16
3.091
0.001
3.291
636.578
31.6
12.924
8.61
6060
6.869
..com
5.959
5-408
5.041
B
4.781
4-587
4-437
4-318
4.221
4-14
4.073
4.015
3.965
3.922
3.883
a sc
3.85
0 810
3.819
3-792
3.768
3.745
3.725
3-707
2 680
3.689
3.674
2.66
3.66
3.646
3-46
3-373
3.291

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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