A random number generator is supposed to produce random numbers that are uniformly distributed on the interval from 0 to 1 . If this is true, the numbers generated come from a population with μ=0.5 and σ=0.2887 . A command to generate 100 random numbers gives outcomes with mean x¯=0.4365 . Assume that the population ?σ remains fixed. We want to test H0:μ=0.5 Ha:μ≠0.5 (a) Calculate the value of the ?z test statistic. (Enter your answer rounded to two decimal places.) z= Between what two numbers does the P‑value lie? A) between 0.02 and 0.04 B) between 0.01 and 0.02 C) between 0.04 and 0.05 D) above 0.25 Between which two Normal critical values z in the bottom row of Table C does z lie? A) below 0.674 B) between 1.036 and 1.282 C) between 1.960 and 2.054 D) between 2.054 and 2.326 (b) Use Table C: Determine whether z is significant at the 5% level (α=0.05 ). A) significant B) not significant (c) Use Table C: Determine whether z is significant at the 1% level (α=0.01 ). A) significant B) not significant (d) Which is an appropriate conclusion for this test? A) We have good evidence at the 5% level that this random number generator is performing properly. B) We have insufficient evidence to say the random number generator is not performing properly. C) We have strong evidence at the 1% level that this random number generator is not performing properly. D) We have good evidence at the 5% level that this random number generator is not performing properly.
A random number generator is supposed to produce random numbers that are uniformly distributed on the interval from 0 to 1 . If this is true, the numbers generated come from a population with μ=0.5 and σ=0.2887 . A command to generate 100 random numbers gives outcomes with mean x¯=0.4365 . Assume that the population ?σ remains fixed. We want to test H0:μ=0.5 Ha:μ≠0.5 (a) Calculate the value of the ?z test statistic. (Enter your answer rounded to two decimal places.) z= Between what two numbers does the P‑value lie? A) between 0.02 and 0.04 B) between 0.01 and 0.02 C) between 0.04 and 0.05 D) above 0.25 Between which two Normal critical values z in the bottom row of Table C does z lie? A) below 0.674 B) between 1.036 and 1.282 C) between 1.960 and 2.054 D) between 2.054 and 2.326 (b) Use Table C: Determine whether z is significant at the 5% level (α=0.05 ). A) significant B) not significant (c) Use Table C: Determine whether z is significant at the 1% level (α=0.01 ). A) significant B) not significant (d) Which is an appropriate conclusion for this test? A) We have good evidence at the 5% level that this random number generator is performing properly. B) We have insufficient evidence to say the random number generator is not performing properly. C) We have strong evidence at the 1% level that this random number generator is not performing properly. D) We have good evidence at the 5% level that this random number generator is not performing properly.
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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Question
A random number generator is supposed to produce random numbers that are uniformly distributed on the interval from 0 to 1 . If this is true, the numbers generated come from a population with μ=0.5 and σ=0.2887 . A command to generate 100 random numbers gives outcomes with mean x¯=0.4365 . Assume that the population ?σ remains fixed. We want to test
H0:μ=0.5
Ha:μ≠0.5
(a) Calculate the value of the ?z test statistic. (Enter your answer rounded to two decimal places.)
z=
Between what two numbers does the P‑value lie?
A) between 0.02 and 0.04
B) between 0.01 and 0.02
C) between 0.04 and 0.05
D) above 0.25
Between which two Normal critical values z in the bottom row of Table C does z lie?
A) below 0.674
B) between 1.036 and 1.282
C) between 1.960 and 2.054
D) between 2.054 and 2.326
(b) Use Table C: Determine whether z is significant at the 5% level (α=0.05 ).
A) significant
B) not significant
(c) Use Table C: Determine whether z is significant at the 1% level (α=0.01 ).
A) significant
B) not significant
(d) Which is an appropriate conclusion for this test?
A) We have good evidence at the 5% level that this random number generator is performing properly.
B) We have insufficient evidence to say the random number generator is not performing properly.
C) We have strong evidence at the 1% level that this random number generator is not performing properly.
D) We have good evidence at the 5% level that this random number generator is not performing properly.
Transcribed Image Text:TABLES
699
Table entry for C is the critical value
t* required for confidence level C.
To approximate one- and two-sided
P-values, compare the value of the t
Tail area
statistic with the critical values of t*
Area C
that match the P-values given at the
bottom of the table.
t*
TABLE C t distribution critical values
Confidence level C
Degrees of
freedom
50%
60%
70%
80%
90%
95%
96%
98%
99%
99.5%
99.8%
99.9%
1
1.000
1.376
1.963
3.078
6.314
12.71
15.89
31.82
63.66
127.3
318.3
636.6
0.816
1.061
1.386
1.886
2.920
4.303
4.849
6.965
9.925
14.09
22.33
31.60
1.250
7.453
5.598
3
0.765
0.978
1.638
2.353
3.182
3.482
4.541
5.841
10.21
12.92
4
0.741
0.941
1.190
1.533
2.132
2.776
2.999
3.747
4.604
7.173
8.610
0.727
0.920
1.156
1.476
2.015
2.571
2.757
3.365
4.032
4.773
5.893
6.869
6.
0.718
0.906
1.134
1.440
1.943
2.447
2.612
3.143
3.707
5.208
4.317
4.029
5.959
7
0.711
0.896
1.119
1.415
1.895
2.365
2.517
2.998
3.499
4.785
5.408
8
0.706
0.889
1.108
1.397
1.860
2.306
2.449
2.896
3.355
3.833
4.501
5.041
9.
0.703
0.883
1.100
1.383
1.833
2.262
2.398
2.821
3.250
3.690
4.297
4.781
10
0.700
0.879
1.093
1.372
1.812
2.228
2.359
2.764
3.169
3.581
4.144
4.587
11
0.697
0.876
1.088
1.363
1.796
2.201
2.328
2.718
3.106
3.497
4.025
4.437
12
0.695
0.873
1.083
1.356
1.782
2.179
2.303
2.681
3.055
3.428
3.930
4.318
13
0.694
0.870
1.079
1.350
1.771
2.160
2.282
2.650
3.012
3.372
3.852
4.221
14
0.692
0.868
1.076
1.345
1.761
2.145
2.264
2.624
2.977
3.326
3.787
4.140
15
0.691
0.866
1.074
1.341
1.753
2.131
2.249
2.602
2.947
3.286
3.733
4.073
16
0.690
0.865
1.071
1.337
1.746
2.120
2.235
2.583
2.921
3.252
3.686
4.015
17
0.689
0.863
1.069
1.333
1.740
2.110
2.224
2.567
2.898
3.222
3.646
3.965
18
0.688
0.862
1.067
1.330
1.734
2.101
2.214
2.552
2.878
3.197
3.611
3.922
1.066
1.064
1.729
1.725
19
0.688
0.861
1.328
2.093
2.205
2.539
2.861
3.174
3.579
3.883
20
0.687
0.860
1.325
2.086
2.197
2.528
2.845
3.153
3.552
3.850
1.063
1.323
3.135
3.527
3.505
21
0.686
0.859
1.721
2.080
2.189
2.518
2.831
3.819
0.858
0.858
22
0.686
1.061
1.321
1.717
2.074
2.183
2.508
2.819
3.119
3.792
23
0.685
1.060
1.319
3.485
1.714
1.711
2.069
2.177
2.500
2.807
3.104
3.768
24
0.685
0.857
1.059
1.318
2.064
2.172
2.492
2.797
3.091
3.467
3.745
25
0.684
0.856
1.058
1.316
1.708
2.060
2.167
2.485
2.787
3.078
3.450
3.725
26
0.684
0.856
1.058
1.315
1.706
2.056
2.162
2.479
2.779
3.067
3.435
3.707
27
0.684
0.855
1.057
1.314
1.703
2.052
2.158
2.473
2.771
3.057
3.421
3.690
28
0.683
0.855
1.056
1.313
1.701
2.048
2.154
2.467
2.763
3.047
3.408
3.674
29
0.683
0.854
1.055
1.311
1.699
2.045
2.150
2.462
2.756
3.038
3.396
3.659
30
0.683
0.854
1.055
1.310
1.697
2.042
2.147
2.457
2.750
3.030
3.385
3.646
40
0.681
0.851
1.050
1.303
1.684
2.021
2.123
2.423
2.704
2.971
3.307
3.551
0.679
0.679
50
0.849
1.047
1.299
1.676
2.009
2.109
2.403
2.678
2.937
3.261
3.496
60
0.848
1.045
1.296
1.671
2.000
2.099
2.390
2.660
2.915
3.232
3.460
80
0.678
0.846
1.043
1.292
1.664
1.990
2.088
2.374
2.639
2.887
3.195
3.416
100
0.677
0.845
1.042
1.290
1.660
1.984
2.081
2.364
2.626
2.871
3.174
3.390
1000
0.675
0.842
1.037
1.282
1.646
1.962
2.056
2.330
2.581
2.813
3.098
3.300
0.674
0.841
1.036
1.282
1.645
1.960
2.054
2.326
2.576
2.807
3.091
3.291
One-sided P
.25
.20
.15
.10
.05
.025
.02
.01
.005
.0025
.001
.0005
Two-sided P
.50
.40
.30
.20
.10
.05
.04
.02
.01
.005
.002
.001
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