Question

The following results are for independent random samples taken from two populations.

Sample 1	Sample 2
n1 = 20	n2 = 30
x1 = 22.9	x2 = 20.1
s1 = 2.6	s2 = 4.8

(c)

At 95% confidence, what is the margin of error? (Round your answer to one decimal place.)

?

(d)

What is the 95% confidence interval for the difference between the two population means? (Use x₁ − x₂. Round your answers to one decimal place.)

? to ?

Answer 1

Answer:

c)

Given,

n₁ = 20

n₂ = 30

x₁ = 22.9

x₂ = 20.1

s₁ = 2.6

s₂ = 4.8

To determine the margin of error at 95% confidence interval

significance level = 0.05

degree of freedom = n1 + n2 - 2

= 20 + 30 - 2

df = 48

critical value t = t 0.05/2 , 48

= t 0.025 , 48

t = 2.01

Now margin of error = t*sqrt(s1^2/n1 + s2^2/n2)

= 2.01*sqrt(2.6^2/20 + 4.8^2/30)

= 2.01*1.0517

Margin of error = 2.1

d)

To determine the 95% confidence interval for the difference between the two population means

Interval = (x1 - x2) +/- margin of error

substitute values

= (22.9 - 20.1) +/- 2.1

= 2.8 +/- 2.1

= (2.8 - 2.1 , 2.8 + 2.1)

Interval = (0.7 , 4.9)