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 16 recent charterholders and computes a mean salary of $200,000 with a standard deviation of $40,000. Use this sample information to determine the 95% 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 :

Given that,

= 200,000

s = 40,000

n = 16

Degrees of freedom = df = n - 1 = 16 - 1 = 15

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,15 =2.131

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

= 2.131 * (40,000 / 16)

= 21314.5954

Margin of error =21314.5954

The 95% confidence interval estimate of the population mean is,

- E < < + E

200,000 - 21314.5954 < < 200,000 + 21314.5954

178685.5045 < < 221314.5954

(178685, 221315 )