Question

You want to make a 90% confidence interval for the difference in the percent of stray cats that are fixed and the percent of cats with homes that are fixed. You take samples from each group. For stray cats you get LaTeX: X_1=3,n_1=20X 1 = 3 , n 1 = 20. For cats with homes, you get LaTeX: X_2=35,n_2=40X 2 = 35 , n 2 = 40. You decide to use the Plus Four method. Fill in the blanks for the values velow, as you would put them into your formula (or calculator) in order to use the Plus Four method.

LaTeX: X_1=X 1 = , LaTeX: n_1=n 1 =

LaTeX: X_2=X 2 = , LaTeX: n_2=

Answer 1

since for plus 4 method: we add 1 in sample success and 2 in total sample size

therefore from above"

x1 =4   ; n1=22

x2 =36 ; n2=42

estimated diff. in proportion=p̂1-p̂2=

-0.6753

Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =

0.0984

for 90 % CI value of z=		1.645	from excel:normsinv((1+0.9)/2)
margin of error E=z*std error =		0.161810
lower bound=(p̂1-p̂2)-E=		-0.8371
Upper bound=(p̂1-p̂2)+E=		-0.5135
from above 90% confidence interval for difference in population proportion =(-0.8371 ,-0.5135)