Question

Assume that a sample is used to estimate a population mean μ. Find the margin of error M.E. that corresponds to a sample of size 14 with a mean of 21.6 and a standard deviation of 12.6 at a confidence level of 99%.Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.

Answer 1

Answer: 16.2

Step-by-step explanation:

Margin of Error formula :-

$E=z_{\alpha/2}\times\dfrac{\sigma}{\sqrt{n}}$

Given : Sample size : n= 4

Mean : $\mu=21.6$

Standard deviation: $\sigma=12.6$

Significance level : $\alpha:1-0.99=0.01$

Now, the margin of error for the sample :-

$E=z_{0.005}\times\dfrac{12.6}{\sqrt{4}}\\\\\Rightarrow\ (2.576)\times6.3$                 [by using standard normal distribution table]

$=16.2288\approx16.2$

Hence, the margin of error for the given sample =16.2