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 36 recent charterholders and computes a mean salary of $162,000 with a standard deviation of $36,000. Use this sample information to determine the lower bound of the 90% confidence interval for the average salary of a CFA® charterholder. (Round the "t" value to 3 decimal places)

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = $162000

sample standard deviation = s = $36000

sample size = n = 36

Degrees of freedom = df = n - 1 = 36 - 1 = 35

At 90% confidence level the t is ,

t = 1 - 90% = 1 - 0.90 = 0.1

t_,df = t_0.1,35 = 1.306

Margin of error = E = t,_df * (s / $\sqrt$ n)

= 1.306 * (36000 / $\sqrt$ 36)

Margin of error = E = 7836

The 90% lower confidence level $\mu$ is,

$\bar x$ - E

162000 - 7836

154164

The lower bound of the interval is 154164