Question

You need to compute the 99% confidence interval for the population mean. How large a sample should you draw to ensure that the sample mean does not deviate from the population mean by more than 2.3

Answer 1

Answer: 60

Step-by-step explanation:

Formula to find sample size :$n=(\dfrac{z^c\times\sigma}{E})^2$, where $z^c$ = critical z value , E -= Margin of error, $\sigma$ = population standard deviation.

Given: E= 2.3

Critical z-value for 99% confidence level = 2.576

$\sigma=6.9$

Then, required sample size :

$n=(\dfrac{6.9\times2.576}{2.3})^2=(7.728)^2\\\\=59.72\approx60$

Hence, the required sample size = 60