Question

Consider the following results for two independent random samples taken from two populations. Sample 1 Sample 2 n 1 = 50 n 2 = 30 x 1 = 13.8 x 2 = 11.5 σ 1 = 2.4 σ 2 = 3.4 What is the point estimate of the difference between the two population means? (to 1 decimal) Provide a 90% confidence interval for the difference between the two population means (to 2 decimals). Use z-table. ( , ) Provide a 95% confidence interval for the difference between the two population means (to 2 decimals). Use z-table. If your answer is negative, enter minus (-) sign. ( , )

Answer 1

Given CI level is 0.9, hence α = 1 - 0.9 = 0.1                  
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.64

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(5.76/50 + 11.56/30)
sp = 0.7075
                  
                  
Margin of Error                  
ME = zc * sp                  
ME = 1.64 * 0.7075                  
ME = 1.16                  
                  
CI = (x1bar - x2bar -zc * sp , x1bar - x2bar + zc * sp)                  
CI = (13.8 - 11.5 - 1.64 * 0.7075 , 13.8 - 11.5 - 1.64 * 0.7075                  
CI = (1.14 , 3.46)

b)

Given CI level is 0.95, hence α = 1 - 0.95 = 0.05                  
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 1.96                  
                  
Margin of Error                  
ME = zc * sp                  
ME = 1.96 * 0.7075                  
ME = 1.387                  
                  
CI = (x1bar - x2bar - zc * sp , x1bar - x2bar + zc * sp)                  
CI = (13.8 - 11.5 - 1.96 * 0.7075 , 13.8 - 11.5 - 1.96 * 0.7075                  
CI = (0.91 , 3.69)