2) To estimate the mean size of maple trees in a certain area of the Adirondacks
ID: 3294377 • Letter: 2
Question
2) To estimate the mean size of maple trees in a certain area of the Adirondacks. A sample of 15 maple tree heights is collected (assume population tree heights is normally distributed).
38
47
28
42
32
38
34
45
40
24
37
49
38
47
47
a) Create a 90% confidence interval for the population mean of maple tree heights.
b) Create a 98% confidence interval for the population mean of maple tree heights.
c) What size sample would you need to estimate the population average heights of the maple trees with an error of 0.2 feet at a 95% confidence (assume population standard deviation is 8.4 feet)
38
47
28
42
32
38
34
45
40
24
37
49
38
47
47
Explanation / Answer
a)for (n-1=14) degree of freedom and 90% CI; t=1.7613
therefore 90% confidence interval for the population mean =sample mean -/+ t*std error =35.7051 ; 42.4282
b)for (n-1=14) degree of freedom and 98% CI; t=2.6245
therefore 90% confidence interval for the population mean =sample mean -/+ t*std error =34.0577 ; 44.0756
c)
here margin of error E =0.2
for 95% CI ; z=1.96
thereofre sample size n=(z*std deviaiton/E)1/2 =~6777
X 38 47 28 42 32 38 34 45 40 24 37 49 38 47 47 mean(X) 39.0667 std deviation(S) 7.3918 std error =S/(n)1/2 1.9085Related Questions
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