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 25 recent charterholders and computes a mean salary of $195,000 with a standard deviation of $40,000. Use this sample information to determine the 90% confidence interval for the average salary of a CFA charterholder. Assume that salaries are normally distributed. (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 is complete but not entirely correct. Confidence interval 181,480 to 208,520

Answer 1

Solution :

t_{$\alpha$ /2,df} = 1.711

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 1.711 * (40000 / $\sqrt$ 25)

Margin of error = E = 13688

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

$\bar x$ - E < $\mu$ < $\bar x$ + E

195000 - 13688 < $\mu$ < 195000 + 13688

181312 < $\mu$ < 208688

CI is : 181312 to 208668