Question

Two random samples are selected from two independent populations. A summary of the samples sizes, sample means, and sample standard deviations is given below: n1=37,n2=44,x¯1=58.9,x¯2=74.7,s1=5.5s2=10.1 n 1 =37, x ¯ 1 =58.9, s 1 =5.5 n 2 =44, x ¯ 2 =74.7, s 2 =10.1 Find a 95.5% confidence interval for the difference μ1−μ2 μ 1 − μ 2 of the means, assuming equal population variances. Confidence Interval

Answer 1

Pooled Variance
sp = sqrt((((n1 - 1)*s1^2 + (n2 - 1)*s2^2)/(n1 + n2 - 2))*(1/n1 + 1/n2))
sp = sqrt((((37 - 1)*5.5^2 + (44 - 1)*10.1^2)/(37 + 44 - 2))*(1/37 + 1/44))
sp = 1.857

Given CI level is 0.955, hence α = 1 - 0.955 = 0.045                  
α/2 = 0.045/2 = 0.0225, tc = t(α/2, df) = 2.037                  
                  
Margin of Error                  
ME = tc * sp                  
ME = 2.037 * 1.857                  
ME = 3.783                  
                  
CI = (x1bar - x2bar - tc * sp , x1bar - x2bar + tc * sp)                  
CI = (58.9 - 74.4 - 2.037 * 1.857 , 58.9 - 74.4 - 2.037 * 1.857                  
CI = (-19.283 , -11.717)