Question

Consider the following results for independent random samples taken from two populations.

Sample 1	Sample 2
n1= 20	n2 = 40
x1= 22.1	x2= 20.6
s1= 2.9	s2 = 4.3

a. What is the point estimate of the difference between the two population means (to 1 decimal)?

b. What is the degrees of freedom for the t distribution (round down)?

c. At 95% confidence, what is the margin of error (to 1 decimal)?

d. What is the 95% confidence interval for the difference between the two population means (to 1 decimal)?

Answer 1

Answer:

a)

Point estimate = x1 - x2

= 22.1 - 20.6

= 1.5

b)

degree of freedom = n1 + n2 - 2

= 20 + 40 - 2

= 58

c)

At 95% confidence, margin of error = z*se

= t(alpha/2,df)*sqrt(s1^2/n1 + s2^2/n2)

= t(0.025,58)*sqrt(2.9^2/20 + 4.3^2/40)

= 2.002*0.9395

= 1.880879

= 1.9

d)

Here 95% CI = point estimate +/- ME

= (1.5 +/- 1.9)

= (-0.4 , 3.4)