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 $158,000 with a standard deviation of $36,000. Use this sample information to determine the 95% confidence interval for the average salary of a CFA charterholder.

Answer 1

Answer: (145820, 170180)

Step-by-step explanation:

Formula for confidence interval for population mean ( when population standard deviation is unknown ) :

$\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}$

, where n= sample size

$\overline{x}$ = sample mean

s= sample standard deviation

$t_{\alpha/2}$= two-tailed t-value for significance level of ($\alpha$).

We assume that  the salary of CFA charterholders is normally distributed .

Let x represents the salary of CFA charterholders .

As per given , we have

n=  36

$\overline{x}=\ 158,000$

Degree of freedom : df = 35    [ df= n-1]

s=  $36,000

Significance level : $\alpha=1-0.95=0.05$

Using t-distribution table ,

$t_{\alpha/2, df}=t_{0.025,\ 35}=2.030$

95% confidence interval for the average salary of a CFA charterholders :-

$158000\pm (2.030)\dfrac{36000}{\sqrt{36}}\\\\=158000\pm 12180\\\\=(158000-12180,158000+12180) =(145820,\ 170180)$

Hence, the 95% confidence interval for the average salary of a CFA charterholder : (145820, 170180)