Consider the following results for two independent random sa

Consider the following results for two independent random samples taken from two populations. n_1 =40 n_2= 35 x bar_1 = 13.2 X bar_2 = 11.4 sigma1 = 2.1 sigma 2 = 3.1 What is the point estimate of the difference between the two population means Provide a 90% confidence interval for the difference between the two population means (to 2 decimals). Provide a 95% confidence interval for the difference between the two population means (to 2 decimals).

Solution

a). point estimate of the difference

= 13.2-11.4

= 1.8

b).

90% CI

Z value for 90% CI =1.645

Standard error = sqrt(2.1²/40 +3.1²/35)) =0.6203

Margin of error =1.6405*0.6203=1.0204

90% CI =1.8±1.0204

=(0.7796, 2.8204)

Answer: (0.78, 2.82) ( two decimals)

c).

95% CI

Z value for 95% CI =1.96

Standard error = sqrt(2.1²/40 +3.1²/35)) =0.6203

Margin of error =1.96*0.6203=1.2158

90% CI =1.8±1.2158

=(0.5842, 3.0158)

Answer: (0.58, 3.02) ( two decimals)