Question

he following results come from two independent random samples taken of two populations.

Sample 1 n1 = 60, x1 = 13.6, σ1 = 2.4

Sample 2 n2 = 25, x2 = 11.6,σ2 = 3

(a) What is the point estimate of the difference between the two population means? (Use x1 − x2.)

(b) Provide a 90% confidence interval for the difference between the two population means. (Use x1 − x2. Round your answers to two decimal places.)

(BLANK) to (BLANK)

(c) Provide a 95% confidence interval for the difference between the two population means. (Use x1 − x2. Round your answers to two decimal places.)

(BLANK) to (BLANK)

Answer 1

a)

Point estimate = 13.6 - 11.6 = 2

b)

Given CI level is 0.9, hence α = 1 - 0.9 = 0.1                  
α/2 = 0.1/2 = 0.05, zc = z(α/2, df) = 1.64
          
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(5.76/60 + 9/25)
sp = 0.6753
      
                  
Margin of Error                  
ME =zc * sp                  
ME = 1.64 * 0.6753                  
ME = 1.107                  
                  
CI = (x1bar - x2bar - tc * sp , x1bar - x2bar + tc * sp)                  
CI = (13.6 - 11.6 - 1.64 * 0.6753 , 13.6 - 11.6 - 1.64 * 0.6753                  
CI = (0.89 , 3.11)  

c)

              
Given CI level is 0.95, hence α = 1 - 0.95 = 0.05                  
α/2 = 0.05/2 = 0.025, zc = z(α/2, df) = 1.96                  
                  
Margin of Error                  
ME = zc * sp                  
ME = 1.96 * 0.6753                  
ME = 1.324                  
                  
CI = (x1bar - x2bar - tc * sp , x1bar - x2bar + tc * sp)                  
CI = (13.6 - 11.6 - 1.96 * 0.6753 , 13.6 - 11.6 - 1.96 * 0.6753                  
CI = (0.68 , 3.32)