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 38 recent CFAs with a mean salary of $138,000 and a standard deviation of $34,000. A sample of 80 MBAs results in a mean salary of $130,000 with a standard deviation of $46,000. Use Table 2. 
μ_{1} is the population mean for individuals with a CFA designation and μ_{2} is the population mean of individuals with MBAs. Let CFAs and MBAs represent population 1 and population 2, respectively. 
a1. 
Set up the hypotheses to test if a CFA designation is more lucrative than an MBA at the 5% significance level. Do not assume that the population variances are equal. 


a2. 
Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) 
Test statistic 
a3.  Approximate the pvalue.  

a4.  Do you reject the null hypothesis at the 5% level?  

b.  Using the critical value approach, can we conclude that CFA is more lucrative?  

H_{0}: μ_{1} − μ_{2} ≤ 0; H_{A}: μ_{1} − μ_{2} > 0
Test Statistic :
t = 1.0608
Test Criteria :
Reject null hypothesis if
DF = 95
No, since the value of the test statistic is less than the critical value of 1.661.
Result : Fail to Reject Null Hypothesis
Decision based on P value
P  value = P ( t > 1.0608 ) = 0.1457
pvalue ≥ 0.10
Reject null hypothesis if P value <
level of significance
P  value = 0.1457 > 0.05 ,hence we fail to reject null
hypothesis
No, since the pvalue is more than α.
Conclusion : We Accept H0
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