construct a 90 confidence interval for u1u2 with the sample

construct a 90% confidence interval for u1-u2 with the sample statistics for mean cholesterol content of a hamburger from two fast food chains and confidence interval construction formula below; assume the populations are approximately normal with unequal variances x1= 108 mg s1= 3.97 mg n1=11 x2= 86mg s2=2.21 mg n2= 14

Solution

standard deviation of sampling distribution

=sqrt (s1ˆ2/n1 + s2ˆ2/n2)

= sqrt ( 3.97ˆ2/11 + 2.21ˆ2/14)

= 1.3345

confidence = mean +/- z-score * std

=>

= (108-86) + / - 1.645 * 1.3345

= (19.808 ,24.195)