Summary statistics are given for independent simple random s

Summary statistics are given for independent simple random samples from two populations. Use the nonpooled t-interval procedure to obtain the specified confidence interval.

Sample mean 1= 76.3, s₁ = 4.5, n₁ = 11,

Sample mean 2 = 65.7, s₂ = 5.1, n₂ = 998% confidence interval

What is your answer?

a) 5.05 to 16.15

b) 5.12 to 16.08

c) 4.98 to 16.22

d) 5.28 to 15.92

Solution

The degree of freedom =n1+n2-2= 11+9-2 = 18

Given a=1-0.98 = 0.02, t(0.01, df=18) =2.55 (from student t table)

So the lower bound is

(xbar1-xbar2) - t*sqrt(s1^2/n1+s2^2/n2)

=(76.3-65.7)-2.55*sqrt(4.5^2/11+5.1^2/9)

=5.053583

So the upper bound is

(xbar1-xbar2) + t*sqrt(s1^2/n1+s2^2/n2)

=(76.3-65.7)+2.55*sqrt(4.5^2/11+5.1^2/9)

=16.14642

Answer: a) 5.05 to 16.15