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 $139,000 with a standard deviation of $25,000. 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.)

Confidence interval to. .

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 139000

sample standard deviation = s = 25000

sample size = n = 25

Degrees of freedom = df = n - 1 = 25 - 1 = 24

At 90% confidence level

= 1 - 90%

=1 - 0.90 = 0.10

/2 = 0.05

t/2,df = t_0.05,24 = 1.711

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

= 1.711 * ( 25000 / 25)

Margin of error = E = 8555

At 90% confidence interval estimate of the population mean is,

- E < < + E

139000 - 8555 < < 139000 + 8555

130445 < < 147555

( 130445 , 147555 )

The 90% confidence interval of the population mean is : ( 130445 , 147555 )