A forestry researcher wants to estimate the average height oftrees in a forest n

Question

A forestry researcher wants to estimate the average height oftrees in a forest near Atlanta, Georgia. She takes a random sampleof 22 trees from this forest. From this sample she found that theaverage height was 4.5 meters with a standard deviation of 0.25meters. Assume that the distribution of the heights of these treesare not strongly skewed and do not have any outliers.

For this confidence interval, what is the value of t?1

What is the value of the standard error, sxbar?2

Finally, what are the bounds of the confidence interval?
Lower bound: 3
Upper bound: 4

Explanation / Answer

Given n=22, xbar=4.5, s=0.25 =0.05 For this confidence interval, what is the value of t? t(0.025, df=n-1=22-1=21)=2.08 (check student t table) What is the value of the standard error,sxbar?s/n = 0.25/sqrt(22) =0.0533 Lower bound: xbar-t*s/n = 4.5- 2.08*0.0533 = 4.3891 Upper bound: xbar+t*s/n =4.5+2.08*0.0533= 4.6109

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