Question

A study compares the rates of growth of vegetation at four swampy undeveloped sites using leaf lengths of a particular species. The table below summarizes the information.

Location	Sample size	Mean (?¯?x¯i)	Std. Dev (??si)
1	6	6.12	0.235
2	6	5.75	0.349
3	6	5.45	0.404
4	6	3.7	0.287

Note that the pooled standard deviation (?s) is 0.325.

a) What is the 90% confidence interval for location 1?
(  ,  )
b) What is the 95% confidence interval for location 2?
(  ,  )
c) What is the 99% confidence interval for the difference between location 3 and location 4?
(  ,  )

Answer 1

a)

pooled standard deviation=Sp =√MSE=

0.325

critical t with 90% CI level and 20 df=

1.725

90% confidence interval for location 1 =6.12 -/+ 1.725*0.325/sqrt(6) =6.12 -/+ 0.229=5.891 to 6.349

b)

critical t with 95% CI level and 20 df=

2.086

   95% confidence interval for location 1 =5.75 -/+ 2.086*0.325/sqrt(6) =5.473 to 6.027

c)

critical t with 99% level and 20 df=

2.845

99% confidence interval =(5.45-3.7) -/+ 2.845*sqrt(1/6+1/6) =1.216 to 2.284