A forestry researcher wants to estimate the average height of trees in a forest

Question

A forestry researcher wants to estimate the average height of trees in a forest near Atlanta, Georgia. She takes a random sample of 25 trees from this forest. From this sample she found that the average height was 4.1 meters with a standard deviation of 0.25 meters. Assume that the distribution of the heights of these trees are 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=25, xbar=4.1, s=0.25
a=0.2
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For this confidence interval, what is the value of t? 1

t(0.1,df=n-1=24)=1.32 (check student t table)
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What is the value of the standard error, sxbar? 2
standard error = s/n = 0.25/5=0.05
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Finally, what are the bounds of the confidence interval?

Lower bound: xbar - t*s/n =4.1 -1.32*0.05 =4.034

Upper bound: xbar - t*s/n=4.1 +1.32*0.05 = 4.166

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