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

Here we use T test to find the confidence interval beacuse we have given not given the Population Standard deviation ( )

sample size = n = 36

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

c = level of confidence = 0.99   (99% is converted into decimal )

Formula of the confidence interval

Where

E = margin of error

t_{(c , n-1 )} = critical value from t table

We calcualte the critical value first

t_{(0.99 , 35 )} = 2.724

We get margin of error as

E = 10442

So 99% confidence interval is

Final answer :-

Required 99% confidence interval is

(135558 , 156442 )