To test Ho: μ = 105 versus H₁: μ#105 a simple random sample of size n = 35 is obtained. Complete parts a through e below. Click here to view the t-Distribution Area in Right Tail. (a) Does the population have to be normally distributed to test this hypothesis? Why? O A. No, because the test is two-tailed. OB. No, because n ≥ 30. OC. Yes, because n ≥ 30. OD. Yes, because the sample is random.
To test Ho: μ = 105 versus H₁: μ#105 a simple random sample of size n = 35 is obtained. Complete parts a through e below. Click here to view the t-Distribution Area in Right Tail. (a) Does the population have to be normally distributed to test this hypothesis? Why? O A. No, because the test is two-tailed. OB. No, because n ≥ 30. OC. Yes, because n ≥ 30. OD. Yes, because the sample is random.
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
Transcribed Image Text:df 0.25
0.20 0.15 0.10
0.05
3.078 6.314
1.886 2.920
1.638 2.353
1.533 2.132
1.156 1.476 2.015
1.134 1.440 1.943
4.029
3.833
3.690
3.581
3.497
3.428
3.372
2.145 2.264 2.624 2.977 3.326
2.131 2.249 2.602
2.947
3.286
2.120 2.235 2.583 2.921
1 1.000 1.376 1.963
2 0.816 1.061 1.386
3 0.765 0.978 1.250
4 0.741 0.941 1.190
5 0.727 0.920
6 0.718 0.906
2.447
2.612 3.143 3.707 4.317
7 0.711 0.896 1.119 1.415 1.895 2.365 2.517 2.998 3.499
8 0.706 0.889 1.108 1.397 1.860 2.306 2.449 2.896 3.355
9 0.703 0.883 1.100 1.383 1.833 2.262 2.398 2.821 3.250
10 0.700 0.879 1.093 1.372 1.812 2.228 2.359 2.764 3.169
11 0.697 0.876 1.088 1.363 1.796 2.201 2.328 2.718 3.106
12 0.695 0.873 1.083 1.356 1.782 2.179 2.303 2.681 3.055
13 0.694 0.870 1.079 1.350 1.771 2.160 2.282 2.650 3.012
14 0.692 0.868 1.076 1.345 1.761
15 0.691
0.866 1.074 1.341 1.753
16 0.690
0,865
1.071 1.337 1.746
0.863 1.069 1.333 1.740 2.110
0.862 1.067 1.330 1.734 2.101 2.214 2.552
1.066 1.328 1.729 2.093 2.205 2.539 2.861
1.064 1.325 1.725 2.086 2.197 2.528 2.845
1.063 1.323 1.721 2.080 2.189 2518 2.831
1.061 1.321 1.717 2.074
1.060 1.319 1.714 2.069 2.177 2.500
1.059 1.318 1.711 2.064 2.172 2.492
1.058 1.316 1.708 2,060 2.167 2.485 2.787
1.058 1.315 1.706 2.056 2.162 2.479 2.779
1.057 1.314 1.703 2.052 2.158 2.473 2.771
1.056 1.313 1.701 2.048 2.154 2.467 2.763
1.055 1.311 1.699 2.045 2.150 2.462 2.756
1.055 1.310 1.697 2.042 2.147 2.457 2.750
1.054
2,040 2.144 2.453 2.744 3.022
1.054 1.309
2.141
2.224 2.567
2.898
2.878
2.183
2.508
2.819
2.807
2.797
17 0.689
18 0.688
19 0.688 0.861
0.687 0.860
0.686 0.859
0.686 0.858
0.685 0.858
0.685 0.857
0.684 0.856
0.684 0.856
0.684 0.855
0.683 0.855
0.683 0.854
0.683 0.854
0.853
0.853
1.309 1.696
1.694
2.037
2.449 2.738
3.015
2.035
2.445 2.733
1.307 1.691
1.306 1.690
35
36 0.681
37 0.681
38 0.681
0.682 0.853
0.682 0.852
0.682 0.852
0.852
0.851
0.851
2.138
2.136 2.441 2.728
2.133 2.438 2.724
2.131
2.129 2.431 2.715
2.127 2.429 2.712
2.125 2.426 2.708
1.053 1.308 1.692
1.052
2.032
1.052
2.030
1.052
1.306 1.688 2.028
1.051 1.305 1.687 2.026
1.051 1.304 1.686 2.024
39 0.681 0.851 1.050 1.304 1.685 2.023
40 0.681 0.851 1.050 1.303 1.684
50 0.679 0.849 1.047 1.299 1.676
60 0.679 0.848 1.045
70 0.678 0.847 1.044
8O 0.678 0.846 1.043
90 0.677 0.846 1.042 1291
100
1000
2.021
2.123
2.423
2.704
2.009
2.000
1.296 1.671
1.294 1.667 1.994
1.292 1.664 1.990
0.677 0.845 1.042 1.290
0.675 0.842 1.037 1.282
0.674 0.842 1.036 1.282
0.25 0.20
0.15
678920 2123425 267890 HSBH5 跖初粥期
30
31 0.682
32 0.682
1-Distribution
Area in Right Tail
df
0.025 0.02
12.706 15.894
4.303 4.849
3.182
2.776
2.571
0.01 0.005 0.0025
0.001
31.821 63.657 127.321 318.309
6.965
9,925
14.089
22.327
3.482 4.541 5.841 7.453
2.999 3.747 4.604
2.757 3.365 4.032
5.598
4.773
2.109
2.099
2.403 2.678
2.390 2.660
2.093 2.381 2.648
2.088
2.374
2.639
2.368
2.632
1.662 1.987 2.084
1.660
1.646
1.645
0.10 0.05 0.025
1.984
2.081
1.962
2.056
1.960 2.054
0.02
3.135
3.119
3.104
3.091
3.078
3.067
3.057
3.047
3.038
3.030
3.008
3.002
2.996
2.434 2.719 2.990
2.985
3.252
3.222
3.197
3.610
3.174
3.579
3.153 3.552
2.980
2.976
2.971
2.937
2.915
2.899
2.887
2.878
10.215
7.173
5.893
2.364 2.626
2.871
2.330
2.581
2.813
2.326
2.576
2.807
0.01 0.005 0.0025
5.208
4.785
4.501
4.297
4.144
4.025
3.930
3.852
3.787
3.733
3.686
3.646
3.527
3.505
3.485
3.467
3.450
3.435
3.421
3.408
3.396
3.385
3.375
3.365
3.356
3.348
3.340
3.333
3.326
3.319
3.313
3.307
3.261
3.232
3.211
3.195
3.183
3.174
3.098
3.090
0.001
0.0005 df
636.619 1
31.599 2
12.924 3
8.610 4
6.869 5
5.959
5.408
5.041
4.781
4.587
4.437
4.318
4.221
4.140
4.073
3.819
3.792
3.768
4.015
16
3.965 17
3.922
18
19
3.883
3.850 20
3.745
3.725
3.707
3.690
3.674
3.659
3.646
3.633
3.622
3.611
3.601
3.591
3.582
3.574
6
7
8
9
3.566
10
11
12
13
14
15
12BU5 SYSNA HRBUS 跖初粥
22
23
24
26
27
28
29
30
31
32
33
34
35
36
37
38
3.558 39
3.551 40
3.496 50
3.460 60
3.435 70
3.416 20
3.402
90
3.390 100
3.300 1000
3.291 z
0.0005df
Transcribed Image Text:To test Ho: μ = 105 versus H₁: µ ‡ 105 a simple random sample of size n = 35 is obtained. Complete parts a through e below.
Click here to view the t-Distribution Area in Right Tail.
(a) Does the population have to be normally distributed to test this hypothesis? Why?
A. No, because the test is two-tailed.
B. No, because n ≥ 30.
C. Yes, because n ≥ 30.
O D. Yes, because the sample is random.
Expert Solution
Step 1: Define the concept central limit theorem
Central limit theorem:
If the size of the samples taken from the population are sufficiently large (>30) then the mean of all the samples taken would be approximately same as the population mean.
The conditions are,
- The population is normal.
- The sample size is≥ 30.
- If the original population doesn’t’ follows normality, for the large n, the sample mean also follows normality.
- The formula of the standard deviation of sampling distribution is σ/√n if n is large even though population does not follows normality.
.
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