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 $146,000 with a standard deviation of $23,000. Use this sample information to determine the 99% confidence interval for the average salary of a CFA charterholder. Assume that salaries are normally distributed. (You may find it useful to reference the t table. Round intermediate calculations to at least 4 decimal places. Round "t" value to 3 decimal places and final answers to the nearest whole number.)

Answer 1

solution

n = 36

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

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2  df = t0.005,35 = 2.724 ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 2.724* ( 23000/ 36) = 10442

The 99% confidence interval estimate of the population mean is,

- E < < + E

146000 - 10442< < 146000+10442

135558< < 156442

( 135558, 156442)