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:
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)
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