DO NOT copy and paste errors from the console. If you messed up, that is fine bu

Question

DO NOT copy and paste errors from the console. If you messed up, that is fine but do not give me your errors, delete them from the document before uploading A studyl of 584 longleaf pine trees in the Wade Tract in Thomas County, Georgia had several purposes. To see if there is a difference in their sizes (in diameters) in two separate areas of the Wade Tract (northern and southern areas), a random sample of 30 trees from the northern area and 30 trees from the southern area was taken. Diameter c (27.8, 14.5, 39.1, 3.2, 58.8, 55.5, 25, 5.4, 19, 30.6, 15.1, 3.6, 28.4, 15, 2.2, 14.2, 44.2, 25.7, 11.2, 46.8, 36.9, 54.1, 10.2, 2.5, 13.8, 43.5, 13.8, 39.7, 6.4, 4.8, 44.4, 26.1, 50.4, 23.3, 39.5, 51, 48.1, 47.2, 40.3, 37.4, 36.8,21.7, 35.7, 32, 40.4, 12.8, 5.6, 44.3, 52.9, 38, 2.6, 44.6, 45.5, 29.1, 18.7, 7, 43.8, 28.3, 36.9, 51.6) Direction = c (rep(North', each-30), rep('South', each-30)) Trees data.frame (diameter.direction) a) Estimate the true difference in mean tree sizes between the northern and southern parts of the Wade Tract with 95% confidence. Interpret. b) Is there a significant difference in the mean diameter of trees in the north versus the trees in the south? Conduct hypothesis test. c) State the kind of error could have been made in context of the problem. The summary statistics are as follows:- ni Si North 30 23.717.5 South 30 34.53 14.258 R code:- t.test(num~cat,alternative-",conf.level-0.95) num: numerical variable name cat: categorical variable name alternative: 'less: , 'two.sided' (default, also for Cls): conf.level: I- (default is 0.95 for = 0.05)

Explanation / Answer

R- Code

s=c(27.8,14.5,39.1,3.2,58.8,55.5,25,5.4,19,30.6,15.1,3.6,28.4,15,2.2,14.2,44.2,25.7,11.2,46.8,36.9,54.1,10.2,2.5,13.8,43.5,13.8,39.7,6.4,4.8,44.4,26.1,50.4,23.3,39.5,51,48.1,47.2,40.3,37.4,36.8,21.7,35.7,32,40.4,12.8,5.6,44.3,52.9,38,2.6,44.6,45.5,29.1,18.7,7,43.8,28.3,36.9,51.6)
s
length(s)
s1=s[1:30]
length(s1)
s1
s2=s[31:60]
length(s2)
s2
summary(s1)
summary(s2)
t.test(s1,s2)

___________________________________________________________________________________________

R-code with Output

> s=c(27.8,14.5,39.1,3.2,58.8,55.5,25,5.4,19,30.6,15.1,3.6,28.4,15,2.2,14.2,44.2,25.7,11.2,46.8,36.9,54.1,10.2,2.5,13.8,43.5,13.8,39.7,6.4,4.8,44.4,26.1,50.4,23.3,39.5,51,48.1,47.2,40.3,37.4,36.8,21.7,35.7,32,40.4,12.8,5.6,44.3,52.9,38,2.6,44.6,45.5,29.1,18.7,7,43.8,28.3,36.9,51.6)
> s
[1] 27.8 14.5 39.1 3.2 58.8 55.5 25.0 5.4 19.0 30.6 15.1 3.6 28.4 15.0 2.2
[16] 14.2 44.2 25.7 11.2 46.8 36.9 54.1 10.2 2.5 13.8 43.5 13.8 39.7 6.4 4.8
[31] 44.4 26.1 50.4 23.3 39.5 51.0 48.1 47.2 40.3 37.4 36.8 21.7 35.7 32.0 40.4
[46] 12.8 5.6 44.3 52.9 38.0 2.6 44.6 45.5 29.1 18.7 7.0 43.8 28.3 36.9 51.6
> length(s)
[1] 60
> s1=s[1:30]
> length(s1)
[1] 30
> s1
[1] 27.8 14.5 39.1 3.2 58.8 55.5 25.0 5.4 19.0 30.6 15.1 3.6 28.4 15.0 2.2
[16] 14.2 44.2 25.7 11.2 46.8 36.9 54.1 10.2 2.5 13.8 43.5 13.8 39.7 6.4 4.8
> s2=s[31:60]
> length(s2)
[1] 30
> s2
[1] 44.4 26.1 50.4 23.3 39.5 51.0 48.1 47.2 40.3 37.4 36.8 21.7 35.7 32.0 40.4
[16] 12.8 5.6 44.3 52.9 38.0 2.6 44.6 45.5 29.1 18.7 7.0 43.8 28.3 36.9 51.6
> summary(s1)
Min. 1st Qu. Median Mean 3rd Qu. Max.
2.20 10.45 17.05 23.70 38.55 58.80
> summary(s2)
Min. 1st Qu. Median Mean 3rd Qu. Max.
2.60 26.65 37.70 34.53 44.55 52.90
> t.test(s1,s2)

Welch Two Sample t-test

data: s1 and s2
t = -2.6286, df = 55.725, p-value = 0.01106
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-19.090199 -2.576468
sample estimates:
mean of x mean of y
23.70000 34.53333

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