Question

Basic Computation: Confidence Interval for My – M2 Consider two inde- pendent normal distributions. A random sample of size n = 20 from the fire distribution showed x = 12 and a random sample of size n2 = 25 from the second distribution showed X2 = 14.

Answer 1

Answer:

a).

when population standard deviation s are known, z distribution is used to construct confidence inter for mean difference.

b).

CI = (21 - 12) = 2 * se

Independent Groups
	Group 1	Group2
	12	14	mean
	3	4	std. dev.
	20	20	n
		-2.000	difference (Group 1 - Group2)
		1.118	standard error of difference
		-3.8390	confidence interval 90.% lower
		-0.1610	confidence interval 90.% upper
		1.8390	margin of error

90% CI for mean difference = (-3.8390, -0.1610).

c).

t distribution is used.

df= n1+n2-2= 20+20-2=38

d).

CI = (21-12) Et * se

mean difference = -2

standard error = 1.118

critical t value at 90% level= 1.686

margin of error = 1.118*1.686 =1.885

lower limit = -2-1.885 = -3.885

upper limit = -2+1.885 = -0.115

f).

yes, with 90% confident we can conclude that µ1 is less than µ2 because both upper and lower limits are negative.