Many species of cuckoos are brood parasites. They lay their eggs in the nests of

Question

Many species of cuckoos are brood parasites. They lay their eggs in the nests of other species. The following data are for the lengths (mm) of cuckoo eggs in a random sample of nests from two different host species. wren: 19.8, 22.1, 21.5, 20.9, 22, 21, 22.3, 21, 20.3, 20.9, 22, 20, 20.8, 21.2, 21 house sparrow: 22, 23.9, 20.9, 23.8, 25, 24, 21.7, 23.8, 22.8, 23.1, 23.1, 23.5, 23, 23 Question 7 (1 point) Question 7 Unsaved Calculate a 95% confidence interval for the mean length of cuckoo eggs for each of the host species. Question 7 options: wren (20.3, 22.0), house sparrow (22.0, 23.9) wren (20.7, 21.5), house sparrow (22.6, 23.7) wren (19.6, 22.6), house sparrow (21.0, 25.2) wren (20.9, 21.3), house sparrow (22.8, 23.4)

Explanation / Answer

wren: n1=15, xbar1=21.12, s1=0.7542262

The degree of freedom =n-1=15-1=14

Given a=0.05, t(0.025, df=14) =2.14 (from standard normal table)

So the lower bound is

xbar - t*s/vn =21.12 - 2.14*0.7542262/sqrt(15) =20.70326

So the upper bound is

xbar + t*s/vn =21.12 + 2.14*0.7542262/sqrt(15) =21.53674

house sparrow: n2=14, xbar2=23.11429, s2=1.049437

The degree of freedom =n-1=14-1=13

t(0.025, df=13) =2.16 (from student t table)

So the lower bound is

xbar - t*s/vn =23.11429 - 2.16*1.049437/sqrt(14) =22.50847

So the upper bound is

xbar + t*s/vn =23.11429 + 2.16*1.049437/sqrt(14) =23.72011

Answer: wren (20.7, 21.5), house sparrow (22.6, 23.7)

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