Question

Construct a? 90% confidence interval for u1 - u2. Two samples are randomly selected from normal populations. The sample statistics are given below. Assume that 2?1= 2?2.

n1=?10, n2=?12, x overbar=?25, x overbar=?23, s1=?1.5, s2=1.9

Answer 1

Solution:
Given in the question that Variance for sample 1 and varaince for sample2 so this is pooled variance t test

Sp²⁼ (n1-1)S1² +(n2-1)S2² /((n1-1)+(n2-1))
Sp^{2 =} ((10-1)*1.5*1.5) +((12-1)*1.9*1.9)/(10-1)+(12-1)) = (20.25+39.71)/20 = 59.96/20 = 2.998

Confidence interval can be calculated as
(X1bar - X2bar) +/- talpha/2 sqrt(Sp² ((1/n1)+(1+n2))
t critical value at df=10+12-2 = 20 and alpha = 0.05 is 1.7247

So confidence interval
(25-23) +/- 1.7247* sqrt(2.998((1/10)+(1/12))
2 +/- 1.7247 * sqrt(0.496333)
2+/- 1.7247*0.7413 = 2+/- 1.2785
So confidence interval is 0.7214 to 3.2785