Question

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, it also entails promising careers with lucrative salaries. 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 $150,000 with a standard deviation of $35,000. Use this sample information to determine the 90% confidence interval for the average salary of a CFA charterholder. Assume that salaries are normally distributed.

Answer 1

Answer:  ($141,775, $158,225)

Step-by-step explanation:

Given : Significance level : $\alpha: 1-0.9=0.1$

Critical value : $z_{\alpha/2}=1.645$

Sample size : n= 49

Sample mean : $\overline{x}=150,000$

Standard deviation : $\sigma=35,000$

The confidence interval for population mean is given by :_

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

$= 150,000\pm (1.645)\dfrac{35000}{\sqrt{49}}\\\\\approx150,000\pm8225\\\\=(150,000-8225,150,000+8225)=(141,775,158,225)$

Hence,he 90% confidence interval for the average salary of a CFA charter-holder = ($141,775, $158,225)