Question

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 34 recent CFAs with a mean salary of $140,000 and a standard deviation of $35,000. A sample of 49 MBAs results in a mean salary of $124,000 with a standard deviation of $22,000.

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 1% significance level.

• H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

• H₀: μ₁ − μ₂ ≥ 0; H_A: μ₁ − μ₂ < 0

• H₀: μ₁ − μ₂ ≤ 0; H_A: 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.)

Test statistic -------

b-2. Find the p-value.

• 0.01 p-value < 0.025

• p-value < 0.01

• p-value  0.10
• 0.05 p-value < 0.10
• 0.025  p-value < 0.05

c. At the 1% significance level, is a CFA designation more lucrative than an MBA?

------- H0. At the 1% significance level. we -------- conclude that the CFA designation is more lucrative than an MBA.

Answer 1

The statistical software output for this problem is:

From above output:

a) H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 0

b - 1) Test statistic = 2.36

b - 2) 0.01 p-value < 0.025

c) Fail to reject; Can't