Test the above hypothesis is a random sample of 250 users has 210 successes. Solution: [Write rules/formula] Calculate p̄ : Calculate Zp : Find Zα : Compare Zp and Zα : 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
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Related questions
Question
Solve the following proportion hypothesis:
Give: Ho: p ≤ 0.6
H1: p > 0.6
A binomial distribution can be approximated with the normal distribution, so use a
z-score for α=0.05.
Test the above hypothesis is a random sample of 250 users has 210 successes.
Solution: [Write rules/formula]
Calculate p̄ :
Calculate Zp :
Find Zα :
Compare Zp and Zα :
Conclusion:
-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
Transcribed Image Text: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
Transcribed Image Text: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
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