Question

We want to estimate the population mean within 5, with a 99% level of confidence. The population standard deviation is estimated to be 15. How large a sample is required? (Round up your answer to the next whole number.)

Answer 1

Answer:  60

Step-by-step explanation:

Formula to calculate sample size (n):

$n=(\dfrac{\sigma\times z^*}{E})^2$

, where $\sigma$ = population standard deviation, E Margin of error , z* = critical value for the confidence interval.

As per given , we have

E =5

$\sigma=15$

Critical value for 99% confidence = 2.576

Then,

$n=(\dfrac{15\times2.576}{5})^2\\\\\Rightarrow\ n=59.721984\approx60$

So, Required sample size = 60 .