Please answer manually and circle the answers. The Chartered Financial Analyst (
ID: 3160054 • Letter: P
Question
Please answer manually and circle the answers.
The Chartered Financial Analyst (CFA®) designation is fast becoming a requirement for serious investment professionals. It is an attractive alternative to getting an MBA for students wanting a career in investment. A student of finance is curious to know if a CFA designation is a more lucrative option than an MBA. He collects data on 37 recent CFAs with a mean salary of $144,000 and a standard deviation of $44,000. A sample of 54 MBAs results in a mean salary of $135,000 with a standard deviation of $21,000. Use Table 2. is the population mean for individuals with a CFA designation and 2 is the population mean of individuals with MBAs.) Let CFAs and MBAs represent population 1 and population 2, respectively. a-1. Set up the hypotheses to test if a CFA designation is more lucrative than an MBA at the 10% significance level. Do not assume that the population variances are equal. a-2. Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.) Test statisticExplanation / Answer
a-1.
Formulating the null and alternative hypotheses,
Ho: u1 - u2 <= 0
Ha: u1 - u2 > 0 [ANSWER, C]
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a-2.
At level of significance = 0.1
As we can see, this is a right tailed test.
Calculating the means of each group,
X1 = 144000
X2 = 135000
Calculating the standard deviations of each group,
s1 = 44000
s2 = 21000
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 37
n2 = sample size of group 2 = 54
Thus, df = n1 + n2 - 2 = 89
Also, sD = 7777.59545
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = 1.157169984 [ANSWER, TEST STATISTIC]
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a-3.
Using tables,
Pvalue > 0.100 [ANSWER, D]
[By technology, the Pvalue is 0.125149616].
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a-4.
As P > 0.05, we do not reject Ho.
Hence, OPTION D. [ANSWER]
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b.
As from the table,
tcrit = 1.300
and t = 1.157 < 1.300, then we fail to reject Ho.
OPTION C. [ANSWER]
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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!