4. Suppose forest researchers are estimating a single population mean of tree di

Question

4. Suppose forest researchers are estimating a single population mean of tree diameters in a certain area under the assumption that population distribution is normal. They measured diameters of a sample of trees and found l the sample mean = 30.5 and 95% confidence interval 29.5, 31.5). Assuming that in the list below you have one and only one 99% confidence interval for the population mean diameter calculated frorn the same sample, circle this 99% confidence interval. (a) (29.7, 31.3) (b) (26, 28) (c) (30.7, 33.3) (d) (29.2, 31.8) (e) (81.5, 34.5) (f) (95, 99)

Explanation / Answer

margin of error=(31.5-29.5)/2 =1

as we know that for 95% CI ; critical z=1.96

and for 99% CI ; critical z =2.576

hence 99% CI =sample mean -/+z*std error =30.5-/+2.576*1/1.96 =29.2 ; 31.8

option D is correct

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