The Chartered Financial Analyst (CFA) designation is fast becoming a requirement for serious investment professionals. Although it requires a successful completion of three levels of grueling exams, the designation often results in a promising career with a lucrative salary. A student of finance is curious about the average salary of a CFA charterholder. He takes a random sample of 25 recent charterholders and computes a mean salary of $140,000 with a standard deviation of $30,000. Use this sample information to determine the 99% confidence interval for the average salary of a CFA charterholder. Assume that salaries are normally distributed. (You may find it useful to reference the t table. Round final answers to nearest whole number.) confidence interval _______to _______.
The Chartered Financial Analyst (CFA) designation is fast becoming a requirement for serious investment professionals. Although it requires a successful completion of three levels of grueling exams, the designation often results in a promising career with a lucrative salary. A student of finance is curious about the average salary of a CFA charterholder. He takes a random sample of 25 recent charterholders and computes a mean salary of $140,000 with a standard deviation of $30,000. Use this sample information to determine the 99% confidence interval for the average salary of a CFA charterholder. Assume that salaries are normally distributed. (You may find it useful to reference the t table. Round final answers to nearest whole number.) confidence interval _______to _______.
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter11: Data Analysis And Displays
Section: Chapter Questions
Problem 10CT
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The Chartered Financial Analyst (CFA) designation is fast becoming a requirement for serious investment professionals. Although it requires a successful completion of three levels of grueling exams, the designation often results in a promising career with a lucrative salary. A student of finance is curious about the average salary of a CFA charterholder. He takes a random sample of 25 recent charterholders and computes a mean salary of $140,000 with a standard deviation of $30,000. Use this sample information to determine the 99% confidence interval for the average salary of a CFA charterholder. Assume that salaries are
confidence interval _______to _______.
Transcribed Image Text:TABLE 2 Student's t Distribution
Entries in this table provide the values of taaf that correspond to a given
upper-tail area a and a specified number of degrees of freedom df. For
example, for a = 0.05 and df = 10, P(Tp2 1.812) = 0.05.
Area In Upper
Tall, a
tar
df
0.20
0.10
0.05
0.025
0.01
0.005
6.314
2.920
1
1.376
3.078
12.706
31.821
63.657
2
1.061
1.886
4.303
6.965
9.925
3.182
4.541
5.841
4.604
3
0.978
1.638
2.353
4
0.941
1.533
2.132
2.776
3.747
0.920
1.476
2.015
2.571
3.365
4.032
1.440
1.415
1.397
6
0.906
1.943
2.447
3.143
3.707
7
0.896
1.895
2.365
2.998
3.499
8
0.889
1.860
2.306
2.896
3.355
9
0.883
1.383
1.833
2.262
2.821
3.250
10
0.879
1.372
1.812
2.228
2.764
3.169
11
0.876
1.363
1.796
2.201
2.718
3.106
12
0.873
1.356
1.782
2.179
2.681
3.055
13
0.870
1.350
1.771
2.160
2.650
3.012
14
0.868
1.345
1.761
2.145
2.624
2.977
15
0.866
1.341
1.753
2.131
2.602
2.947
16
0.865
1.337
1.746
2.120
2.583
2.921
17
0.863
1.333
1.740
2.110
2.567
2.898
18
0.862
1.330
1.734
2.101
2.552
2.878
19
0.861
1.328
1.729
2.093
2.539
2.861
20
0.860
1.325
1.725
2.086
2.528
2.845
21
0.859
1.323
1.721
2.080
2.518
2.831
2.074
2.069
2.064
22
0.858
1.321
1.717
2.508
2.819
23
0.858
1.319
1.714
2.500
2.807
24
0.857
1.318
1.711
2.492
2.797
25
0.856
1.316
1.708
2.060
2.485
2.787
26
0.856
1.315
1.706
2.056
2.479
2.779
2.473
2.467
27
0.855
1.314
1.703
2.052
2.771
28
0.855
1.313
1.701
2.048
2.763
29
0.854
1.311
1.699
2.045
2.462
2.756
30
0.854
1.310
1.697
2.042
2.457
2.750
31
0.853
1.309
1.696
2.040
2.453
2.744
32
0.853
1.309
1.694
2.037
2.449
2.738
2.733
2.728
33
0.853
1.308
1.692
2.035
2.445
34
0.852
1.307
1.691
2.032
2.441
35
0.852
1.306
1.690
2.030
2.438
2.724
1.306
1.305
36
0.852
1.688
2.028
2.434
2.719
37
0.851
1.687
2.026
2.431
2.715
38
0.851
1.304
1.686
2.024
2.429
2.712
39
0.851
1.304
1.685
2.023
2.426
2.708
40
0.851
1.303
1.684
2.021
2.423
2.704
41
0.850
1.303
1.683
2.020
2.421
2.701
42
0.850
1.302
1.682
2.018
2.418
2.698
1.302
1.301
0.850
1.681
1.680
43
2.017
2.416
2.695
44
0.850
2.015
2.414
2.692
1.679
1.679
1.678
45
0.850
1.301
2.014
2.412
2.690
1.300
1.300
2.687
2.685
46
0.850
2.013
2.410
47
0.849
2.012
2.408
0,849
2.407
2.405
48
1.299
1.677
2.011
2.682
49
0.849
1.299
1.677
2.010
2.680
50
0.849
1.299
1.676
2.009
2.403
2.678
1.298
1.298
51
0.849
1.675
2.008
2.402
2.676
52
0.849
1.675
2.007
2.400
2.674
53
0.848
1.298
1.674
2.006
2.399
2.672
54
0.848
1.297
1.674
2.005
2.397
2.670
55
0.848
1.297
1.673
2.004
2.396
2.668
1.297
1.297
56
0.848
1.673
2.003
2.395
2.667
57
0.848
1.672
2.002
2.394
2.665
58
0.848
1.296
1.672
2.002
2.392
2.663
59
0.848
1.296
1.671
2.001
2.391
2.662
60
0.848
1.296
1.671
2.000
2.390
2.660
80
0.846
1.292
1.664
1.990
2.374
2.639
100
0.845
1.290
1.660
1.984
2.364
2.626
150
0.844
1.287
1.655
1.976
2.351
2.609
200
0.843
1.286
1.653
1.972
2.345
2.601
500
0.842
1.283
1.648
1.965
2.334
2.586
1.282
1.282
1000
0.842
1.646
1.962
2.330
2.581
00
0.842
1.645
1.960
2.326
2.576
Source: t values calculated with Excel.
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