Question

A financial analyst wanted to determine the mean annual return on mutual funds. A random sample of 60 returns shows a mean of 12%. If the population standard deviation is assumed to be 4%, estimate with 95% confidence the mean annual return on all mutual funds.

Answer 1

Given that,

$\bar x = 0.12 , \sigma = 0.04$$,n = 60$

At 95% confidence level the z is ,

$\alpha = 1 - 0.95 = 0.05$

$\dfrac{\alpha }{ 2} = \dfrac{0.05 }{ 2} = 0.025$

$Z_{\frac{\alpha}{2}} = Z_{0.025 }= 1.96$

Margin of error $= E = Z_{\frac{\alpha}{2}}\times \dfrac{\sigma }{\sqrt{n}})$

$=1.96\times \dfrac{0.04}{\sqrt{60}}= 0.010$

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

$\bar x - E < \mu < \bar x + E \\ 0.12 - 0.010 < \mu < 0.12 + 0.010 \\ 0.11 < \mu < 0.13 \\ (0.11, 0.13) \\ (11, 13)$

Confidence interval is (11%,13%)