In: Statistics and Probability
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 50 recent CFAs with a mean salary of $140,000 and a standard deviation of $52,000. A sample of 80 MBAs results in a mean salary of $131,000 with a standard deviation of $14,000.
Assume that μ1 is the population mean for
individuals with a CFA designation and μ2 is
the population mean of individuals with MBAs. (You may find
it useful to reference the appropriate table: z table
or t table)
a. Set up the hypotheses to test if a CFA
designation is more lucrative than an MBA at the 10% significance
level.
H0: μ1 − μ2 = 0; HA: μ1 − μ2 ≠ 0
H0: μ1 − μ2 ≥ 0; HA: μ1 − μ2 < 0
H0: μ1 − μ2 ≤ 0; HA: μ1 − μ2 > 0
b-1. Calculate the value of the test statistic. Do not assume that the population variances are equal. (Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
b-2. Find the p-value.
p-value < 0.01
c. At the 10% significance level, is a CFA designation more lucrative than an MBA?