Question

uppose germination periods, in days, for grass seed are normally distributed and have a known population standard deviation of 2 days and an unknown population mean. A random sample of 22 types of grass seed is taken and gives a sample mean of 46 days. Find the error bound (EBM) of the confidence interval with a 90% confidence level. Round your answer to THREE decimal places.

Answer 1

Answer: 0.701

Step-by-step explanation:

Formula :  $EBM =z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$ , where $\alpha=$ significance level , $\sigma =$ Population standard deviation, n= sample size.

As per given,  n= 22

$\sigma = 2$

Critical z- value for 90% confidence level : $z_{\alpha/2}=1.645$

Then,

 $EBM =(1.645)\dfrac{2}{\sqrt{22}}\\\\=(1.645)\dfrac{2}{4.690416}\\\\\approx0.701$

Hence ,  error bound (EBM) of the confidence interval with a 90% confidence level= ± 0.701