10points eBookPrintCheck my workCheck My Work button is now enabled3Item 6The 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 _______. TABLE 2 Student's t DistributionEntries in this table provide the values of taaf that correspond to a givenupper-tail area a and a specified number of degrees of freedom df. Forexample, for a = 0.05 and df = 10, P(Tp2 1.812) = 0.05.Area In UpperTall, atardf0.200.100.050.0250.010.0056.3142.92011.3763.07812.70631.82163.65721.0611.8864.3036.9659.9253.1824.5415.8414.60430.9781.6382.35340.9411.5332.1322.7763.7470.9201.4762.0152.5713.3654.0321.4401.4151.39760.9061.9432.4473.1433.70770.8961.8952.3652.9983.49980.8891.8602.3062.8963.35590.8831.3831.8332.2622.8213.250100.8791.3721.8122.2282.7643.169110.8761.3631.7962.2012.7183.106120.8731.3561.7822.1792.6813.055130.8701.3501.7712.1602.6503.012140.8681.3451.7612.1452.6242.977150.8661.3411.7532.1312.6022.947160.8651.3371.7462.1202.5832.921170.8631.3331.7402.1102.5672.898180.8621.3301.7342.1012.5522.878190.8611.3281.7292.0932.5392.861200.8601.3251.7252.0862.5282.845210.8591.3231.7212.0802.5182.8312.0742.0692.064220.8581.3211.7172.5082.819230.8581.3191.7142.5002.807240.8571.3181.7112.4922.797250.8561.3161.7082.0602.4852.787260.8561.3151.7062.0562.4792.7792.4732.467270.8551.3141.7032.0522.771280.8551.3131.7012.0482.763290.8541.3111.6992.0452.4622.756300.8541.3101.6972.0422.4572.750310.8531.3091.6962.0402.4532.744320.8531.3091.6942.0372.4492.7382.7332.728330.8531.3081.6922.0352.445340.8521.3071.6912.0322.441350.8521.3061.6902.0302.4382.7241.3061.305360.8521.6882.0282.4342.719370.8511.6872.0262.4312.715380.8511.3041.6862.0242.4292.712390.8511.3041.6852.0232.4262.708400.8511.3031.6842.0212.4232.704410.8501.3031.6832.0202.4212.701420.8501.3021.6822.0182.4182.6981.3021.3010.8501.6811.680432.0172.4162.695440.8502.0152.4142.6921.6791.6791.678450.8501.3012.0142.4122.6901.3001.3002.6872.685460.8502.0132.410470.8492.0122.4080,8492.4072.405481.2991.6772.0112.682490.8491.2991.6772.0102.680500.8491.2991.6762.0092.4032.6781.2981.298510.8491.6752.0082.4022.676520.8491.6752.0072.4002.674530.8481.2981.6742.0062.3992.672540.8481.2971.6742.0052.3972.670550.8481.2971.6732.0042.3962.6681.2971.297560.8481.6732.0032.3952.667570.8481.6722.0022.3942.665580.8481.2961.6722.0022.3922.663590.8481.2961.6712.0012.3912.662600.8481.2961.6712.0002.3902.660800.8461.2921.6641.9902.3742.6391000.8451.2901.6601.9842.3642.6261500.8441.2871.6551.9762.3512.6092000.8431.2861.6531.9722.3452.6015000.8421.2831.6481.9652.3342.5861.2821.28210000.8421.6461.9622.3302.581000.8421.6451.9602.3262.576Source: t values calculated with Excel.

Given,sample size(n)=25sample mean(x¯)=140,000standard deviation(s)=30,000degrees of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Item 6

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 _______.

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.

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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