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 49 recent charterholders and computes a mean salary of $100,000 $with a standard deviation of $42,000.$ Use this sample information to determine the 90% confidence interval for the average salary of a CFA charterholder.

Answer:
Given Data:

  • Sample mean $ (\bar{x}) = 100,000 $
  • Sample standard deviation $ (s) = 42,000 $
  • Sample size $ (n) = 49 $
  • Confidence interval level $ = 90% $

Solution:

The significance level:

$ \alpha = 1 – 0.90 = 0.10 $

The degrees of freedom:

$ df = n – 1 = 49 – 1 = 48 $

The critical value:

$ t_c = t_{\frac{\alpha}{2}, df} = t_{0.05, 48} \approx 1.677$

The confidence interval:

$ CI = \bar{x} \pm t_c \times \frac{s}{\sqrt{n}} $

$ = 100,000 \pm 1.677 \times \frac{42,000}{\sqrt{49}} $

$ = (89,938, 110,062) $

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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 49 recent charterholders and computes a mean salary of $100,000 $with a standard deviation of $42,000.$ Use this sample information to determine the 90% confidence interval for the average salary of a CFA charterholder.