Question 4: The table below skhowota of tee becights(n m), siken fcon two sepast
ID: 3374945 • Letter: Q
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Question 4: The table below skhowota of tee becights(n m), siken fcon two sepaste focest areas. Tree heights in these forests are assumed to follow an approximately normal distribution. Forest Area 1 16.3 19.4 17.4 17.8 17.1 17.8 18.2 19.8 13.4 19.0 18.4 17.0 18.4 19.8 13.2 16.4 18.7 18.1 17.6 12 Forest Area 2 19.1 17.8 10.5 17.0 21.8 12.4 15.2 10.9 14.0 14.5 13.9 15.3 14.8 17.0 16.4 13.8 16.5 15.5 15.5 18 a) Calculate 95% and 99% confidence intervals for the difference between the mean tree heights in these 4 two forest areas. b) Comment on what the results from Part (a) suggest about any claims that might be made suggesting that the average tree heights in these two forests are about the same. Explain your answer in reference to the confidence intervals which you calculated.Explanation / Answer
(1-alpha)*100% confidence interval for difeerecneo of population mean=
difference of sample mean±t(alpha/2,n)*SE(difference of sample mean)
SE(difference of sample mean)=((sp*(1/n1 +1/n2)1/2) and
sp2=((n1-1)s12+(n2-1)s22)/n and with df is n=n1+n2-2
t=17.95/7.64=2.35
(a) (1-alpha)*100% confidence interval for difference of population mean=
=difference of sample mean±t(alpha/2,n)*SE(diffefrence of sample mean)
95% confidence interval =17.95±t(0.05/2, n)*7.64=17.95±2.0244*7.64=17.95±15.47=(2.48, 33.42)
99% confidence interval =17.95±t(0.01/2, n)*7.64=17.95±2.71*7.64=17.95±20.71=(-2.66, 38.66)
(b) since 0 does not belongs to 99% confidence interval but belongs to 95% confidence interval, so at 95% confidence interval the heights of two tree height are different and at 99% confidence interval they are same
following information has been generated using ms-excel
sample mean s s2 n (n-1)s2 Driver 173.1 21.05 443.1025 20 8418.9475 conductor 155.15 26.93 725.2249 20 13779.2731 difference= 17.95 1168.3274 40 22198.2206 sp2= 584.16 sp= 24.17 SE(difference) 7.643060251Related Questions
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