the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the exam, scores are normally distributed with μ=525. The teacher obtains a random sample of 2200 students, puts them through the reviewclass, and finds that the mean math score of the 2200 students is 530 with a standard deviation of 112. Complete parts (a) through (d) below. LOADING... Click the icon to view the t-Distribution Area in the Right Tail. (a) State the null and alternative hypotheses. Let μ be the mean score. Choose the correct answer below. A. H0: μ<525, H1: μ>525 B. H0: μ=525, H1: μ>525 C. H0: μ>525, H1: μ≠525 D. H0: μ=525, H1: μ≠525 (b) Test the hypothesis at the α=0.10 level of significance. Is a mean math score of 530 statistically significantly higher than 525? Conduct a hypothesis test using the P-value approach. Find the test statistic. t0= (Round to two decimal places as needed.) Approximate the P-value corresponding to the critical value of t. The P-value is . Is the sample mean statistically significantly higher? Yes No (c) Do you think that a mean math score of 530 versus 525 will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance? No, because the score became only 0.95% greater. Yes, because every increase in score is practically significant. (d) Test the hypothesis at the α=0.10 level of significance with n=350 students. Assume that the sample mean is still 530 and the sample standard deviation is still 112. Is a sample mean of 530 significantly more than 525? Conduct a hypothesis test using the P-value approach. Find the test statistic. t0= (Round to two decimal places as needed.) Approximate the P-value corresponding to the critical value of t. The P-value is Is the sample mean statistically significantly higher? Yes No What do you conclude about the impact of large samples on the P-value? A. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences. B. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences. C. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences. D. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant difference
the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the exam, scores are normally distributed with μ=525. The teacher obtains a random sample of 2200 students, puts them through the reviewclass, and finds that the mean math score of the 2200 students is 530 with a standard deviation of 112. Complete parts (a) through (d) below. LOADING... Click the icon to view the t-Distribution Area in the Right Tail. (a) State the null and alternative hypotheses. Let μ be the mean score. Choose the correct answer below. A. H0: μ<525, H1: μ>525 B. H0: μ=525, H1: μ>525 C. H0: μ>525, H1: μ≠525 D. H0: μ=525, H1: μ≠525 (b) Test the hypothesis at the α=0.10 level of significance. Is a mean math score of 530 statistically significantly higher than 525? Conduct a hypothesis test using the P-value approach. Find the test statistic. t0= (Round to two decimal places as needed.) Approximate the P-value corresponding to the critical value of t. The P-value is . Is the sample mean statistically significantly higher? Yes No (c) Do you think that a mean math score of 530 versus 525 will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance? No, because the score became only 0.95% greater. Yes, because every increase in score is practically significant. (d) Test the hypothesis at the α=0.10 level of significance with n=350 students. Assume that the sample mean is still 530 and the sample standard deviation is still 112. Is a sample mean of 530 significantly more than 525? Conduct a hypothesis test using the P-value approach. Find the test statistic. t0= (Round to two decimal places as needed.) Approximate the P-value corresponding to the critical value of t. The P-value is Is the sample mean statistically significantly higher? Yes No What do you conclude about the impact of large samples on the P-value? A. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences. B. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences. C. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences. D. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant difference
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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Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Question
100%
the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the exam, scores are normally distributed with
μ=525.
The teacher obtains a random sample of
2200
students, puts them through the reviewclass, and finds that the mean math score of the
2200
students is
530
with a standard deviation of
112.
Complete parts (a) through (d) below.LOADING...
(a) State the null and alternative hypotheses. Let
μ
be the mean score. Choose the correct answer below.H0: μ<525,
H1: μ>525H0: μ=525,
H1: μ>525H0: μ>525,
H1: μ≠525H0: μ=525,
H1: μ≠525(b) Test the hypothesis at the
α=0.10
level of significance. Is a mean math score of
530
statistically significantly higher than
525?
Conduct a hypothesis test using the P-value approach.Find the test statistic.
t0=
(Round to two decimal places as needed.)
Approximate the P-value corresponding to the critical value of t.
The P-value is
.
Is the sample mean statistically significantly higher?
Yes
No
(c) Do you think that a mean math score of
530
versus
525
will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance?No, because the score became only
0.95%
greater.Yes, because every increase in score is practically significant.
(d) Test the hypothesis at the
α=0.10
level of significance with
n=350
students. Assume that the sample mean is still
530
and the sample standard deviation is still
112.
Is a sample mean of
530
significantly more than
525?
Conduct a hypothesis test using the P-value approach.Find the test statistic.
t0=
(Round to two decimal places as needed.)
Approximate the P-value corresponding to the critical value of t.
The P-value is
Is the sample mean statistically significantly higher?
Yes
No
What do you conclude about the impact of large samples on the P-value?
As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences.
As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences.
As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences.
As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant difference
Transcribed Image Text:t-Distribution Area in Right Tail
t-Distribution
Arca in Right Tail
df
0,25
(0.20
0.15
0.10
0.05
0.025
0.02
0.01
0.005
0.0025
0,001
0.0005
636.619
31.599
6.314
2.920
2.353
2.132
2.015
15.894
4.849
3.482
2.999
2.757
1.376
3.078
31.821
63.657
9.925
5.841
4.604
4.032
127.321
14.089
7.453
5.598
4.773
318.309
22.327
1.000
0.816
0.765
4
1
1.963
1.386
1.250
1.190
1.156
12.706
4.303
3.182
2.776
2.571
1.061
0.978
0.941
0.920
1.886
1.638
1.533
1.476
6.965
4.541
3.747
3.365
3
10.215
7.173
12.924
0.741
0.727
8.610
5.893
6.869
1.440
1.415
1.397
1.383
1.093 1.372
2.612
2.517
2.449
2.398
2.359
5.959
5.408
5.041
4.781
4.587
0.718
7
1.943
1.895
0.906
2.447
2.365
2.306
2.262
2.228
3.143
2.998
2.896
2.821
2.764
3.707
3.499
3.355
3.250
3.169
4.317
4.029
3.833
5.208
4.785
4.501
4.297
4.144
1.134
0.711
0.706
0.703
0.700
0.896
1.119
1.108
1.100
8
0.889
1.860
0.883
0.879
1.833
3.690
3.581
9.
10
1.812
0.697
0.695
0.694
0.692
0.691
0.876
0.873
0.870
0.868
2.328
2.303
2.282
2.264
2.249
1.363
1.796
1.782
1.771
1.761
1.753
2.201
2.179
2.160
2.145
2.131
2.718
3.106
3.055
3.012
2.977
2.947
3.497
3.428
3.372
3.326
3.286
4.437
4.318
4.221
11
1.088
1.083
1.079
1.076
1.074
4.025
3.930
3.852
3.787
3.733
12
1.356
1.350
1.345
1.341
2.681
2.650
2.624
2.602
13
14
4.140
15
0.866
4.073
1.071
1.069 1.333
1.067
2.235
2.224
2.214
2.205
2.197
2.583
2.567
2.552
2.539
2.528
4.015
3.965
3.922
3.883
3.850
0.690
0.865
0.863
0.862
1.337
1.746
1.740
1.734
1.729
1.725
2.120
2.110
2.101
2.093
2.086
2.921
2.898
2.878
2.861
2.845
3.252
3.222
3.197
3.174
3.153
3.686
3.646
3.610
3.579
3.552
16
17
0.689
18
0.688
1.330
0.688
0.687
19
0.861
1.066
1.328
20
0.860
1.064
1.325
0.859
0.858
0.858
2.189
2.183
2.177
2.172
2.167
1.721
1.717
21
22
23
24
25
2.080
2.074
2.069
2.064
2518
2.508
2.500
2.492
2.485
2.831
2.819
2.807
2.797
2.787
3.135
3.119
3.104
3.091
3.078
3.527
3.505
3.485
3.467
3.450
0.686
1.063
1.061
1.060
1.059
1.058
1.323
1.321
1.319
1.318
1.316
3.819
0.686
0.685
0.685
0.684
1.714
1.711
1.708
3.792
3.768
3.745
3.725
0857
0.856
2.060
26
27
28
29
30
0.856
0.855
0.855
0.854
0.854
1.058
1.057
1.056
1.055
1.055
1.315
1.314
1.313
1.311
1.310
1.706
1.703
1.701
2.056
2.052
2.048
2.045
2.042
2.162
0.684
0.684
0.683
0.683
0.683
2.158
2.154
2.150
2.147
2.479
2.473
2.467
2.462
2.457
2.779
2.771
2.763
2.756
2.750
3.067
3.057
3.047
3.038
3.030
3.435
3.421
3.408
3.396
3.385
3.707
3.690
3.674
3.659
3.646
1.699
1.697
0.682
0.682
0.682
0.682
0.682
0.853
0.853
0.853
0.852
0.852
1.054
1.054
1.053
1.052
1.052
1.309
1.309
1.308
1.307
1.306
1.696
1.694
1.692
1.691
2.040
2.037
2.035
2.032
2.030
2.453
2.449
2.445
2.441
2.438
2.744
2.738
2.733
2.728
2.724
3.022
3.015
3.008
3.375
3.365
3.356
3.348
3.340
3.633
3.622
3.611
3.601
3.591
31
2.144
32
33
34
35
2.141
2.138
2.136
2.133
3.002
2.996
1.690
2.028
2.026
2.024
2.023
2.021
1.688
1.687
36
37
38
39
40
0.852
0.851
0.851
0.851
0.851
3.333
3.326
3.319
3.313
3.307
1.052
1.306
1.051 1.305
1.304
1.304
1.303
2.131
2.129
2.127
2.125
2.123
2.719
2.715
2.990
2.985
2.980
2.976
2.971
3.582
3.574
3.566
3.558
3.551
0.681
0.681
2.434
2.431
2.429
2.426
2.423
0.681
0.681
0.681
1.051
1.050
1.686
1.685
1.684
2.712
2.708
2.704
1.050
0.679
0.679
0.678
0.678
0.677
2.109
2.099
2.093
2.088
0.849
1.047
1.299
1.676
1.671
1.667
1.664
1.662
2.009
2.000
1.994
1.990
1.987
2.403
2.390
2.381
2.374
2.368
2.678
2.660
2.648
2.639
2.632
2.937
2.915
2.899
2.887
2.878
3.261
3.232
3.211
3.195
3.183
3.496
3.460
3.435
3.416
3.402
50
1.045
1.296
1.044 1.294
1.043
60
0.848
0.847
0.846
0.846
70
1.292
1.042 1.291
80
90
2.084
0.677
0.675
0.674
0.845
0.842
0.842
1.042 1.290
1.037
1.282
1.036
1.282
1.984
2.081
2.056
2.054
2.364
2.330
2.326
2.626
2.581
2.576
2.871
2.813
2.807
3.174
3.098
3.090
3.390
3.300
3.291
100
1.660
1000
1.646
1.962
1.960
1.645
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