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 testH0:μ=0.5Ha: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) significantB) not significant (c) Use Table C: Determine whether z is significant at the 1% level (α=0.01 ). A) significantB) 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. TABLES699Table entry for C is the critical valuet* required for confidence level C.To approximate one- and two-sidedP-values, compare the value of the tTail areastatistic with the critical values of t*Area Cthat match the P-values given at thebottom of the table.t*TABLE C t distribution critical valuesConfidence level CDegrees offreedom50%60%70%80%90%95%96%98%99%99.5%99.8%99.9%11.0001.3761.9633.0786.31412.7115.8931.8263.66127.3318.3636.60.8161.0611.3861.8862.9204.3034.8496.9659.92514.0922.3331.601.2507.4535.59830.7650.9781.6382.3533.1823.4824.5415.84110.2112.9240.7410.9411.1901.5332.1322.7762.9993.7474.6047.1738.6100.7270.9201.1561.4762.0152.5712.7573.3654.0324.7735.8936.8696.0.7180.9061.1341.4401.9432.4472.6123.1433.7075.2084.3174.0295.95970.7110.8961.1191.4151.8952.3652.5172.9983.4994.7855.40880.7060.8891.1081.3971.8602.3062.4492.8963.3553.8334.5015.0419.0.7030.8831.1001.3831.8332.2622.3982.8213.2503.6904.2974.781100.7000.8791.0931.3721.8122.2282.3592.7643.1693.5814.1444.587110.6970.8761.0881.3631.7962.2012.3282.7183.1063.4974.0254.437120.6950.8731.0831.3561.7822.1792.3032.6813.0553.4283.9304.318130.6940.8701.0791.3501.7712.1602.2822.6503.0123.3723.8524.221140.6920.8681.0761.3451.7612.1452.2642.6242.9773.3263.7874.140150.6910.8661.0741.3411.7532.1312.2492.6022.9473.2863.7334.073160.6900.8651.0711.3371.7462.1202.2352.5832.9213.2523.6864.015170.6890.8631.0691.3331.7402.1102.2242.5672.8983.2223.6463.965180.6880.8621.0671.3301.7342.1012.2142.5522.8783.1973.6113.9221.0661.0641.7291.725190.6880.8611.3282.0932.2052.5392.8613.1743.5793.883200.6870.8601.3252.0862.1972.5282.8453.1533.5523.8501.0631.3233.1353.5273.505210.6860.8591.7212.0802.1892.5182.8313.8190.8580.858220.6861.0611.3211.7172.0742.1832.5082.8193.1193.792230.6851.0601.3193.4851.7141.7112.0692.1772.5002.8073.1043.768240.6850.8571.0591.3182.0642.1722.4922.7973.0913.4673.745250.6840.8561.0581.3161.7082.0602.1672.4852.7873.0783.4503.725260.6840.8561.0581.3151.7062.0562.1622.4792.7793.0673.4353.707270.6840.8551.0571.3141.7032.0522.1582.4732.7713.0573.4213.690280.6830.8551.0561.3131.7012.0482.1542.4672.7633.0473.4083.674290.6830.8541.0551.3111.6992.0452.1502.4622.7563.0383.3963.659300.6830.8541.0551.3101.6972.0422.1472.4572.7503.0303.3853.646400.6810.8511.0501.3031.6842.0212.1232.4232.7042.9713.3073.5510.6790.679500.8491.0471.2991.6762.0092.1092.4032.6782.9373.2613.496600.8481.0451.2961.6712.0002.0992.3902.6602.9153.2323.460800.6780.8461.0431.2921.6641.9902.0882.3742.6392.8873.1953.4161000.6770.8451.0421.2901.6601.9842.0812.3642.6262.8713.1743.39010000.6750.8421.0371.2821.6461.9622.0562.3302.5812.8133.0983.3000.6740.8411.0361.2821.6451.9602.0542.3262.5762.8073.0913.291One-sided P.25.20.15.10.05.025.02.01.005.0025.001.0005Two-sided P.50.40.30.20.10.05.04.02.01.005.002.001

Name: A random number generator is supposed to produce random numbers that a
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Description: 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 numb

Given information Sample mean x̅ = 0.4365 Population mean µ = 0.5 Sample size = 100 Standard…

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.)

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.

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

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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