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

Explanation:

Formula :
`EBM =z_(\alpha/2)(\sigma)/(√(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)(2)/(√(22))\\\\=(1.645)(2)/(4.690416)\\\\\approx0.701`

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