Question

# The Chartered Financial Analyst (CFA) designation is fast becoming a requirement for serious investment professionals. Although...

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.)

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

Required 99% confidence interval is

(135558 , 156442 )

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