Question

A study aims to compare the size of butterfly wings between two related species eight randomly selected butterflies from each species yield the following wing sizes as measured in centimeters:

Species 1: 4 5 5 3 6 4 5 7

Species 2: 4 3 4 4 3 2 5 4

Calculate a 90% confidence interval estimate for the difference between the mean wing sizes of two species interpret this interval

Answer 1

Confidence interval for difference between two population means of paired samples is given as below:

Confidence interval = Dbar ± t*SD/sqrt(n)

From given data, we have

Dbar = 1.25

Sd = 1.488047618

n = 8

df = n – 1 = 7

Confidence level = 90%

Critical t value = 1.8946

(by using t-table)

Confidence interval = Dbar ± t*SD/sqrt(n)

Confidence interval = 1.25 ± 1.8946*1.488047618/sqrt(8)

Confidence interval = 1.25 ± 0.9967

Lower limit = 1.25 - 0.9967 = 0.2533

Upper limit = 1.25 + 0.9967 = 2.2467

0.2533 < µd < 2.2467