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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.

Respuesta :

JeanaShupp

Answer: 0.701

Step-by-step explanation:

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

As per given,  n= 22

[tex]\sigma = 2[/tex]

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

Then,

 [tex]EBM =(1.645)\dfrac{2}{\sqrt{22}}\\\\=(1.645)\dfrac{2}{4.690416}\\\\\approx0.701[/tex]

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

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