Construct a
99%
confidence interval for
mu 1 minus mu 2μ1−μ2
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.
Stats 
x overbar 1 equals 134 mg comma s 1 equals 3.64 mg comma n 1 equals 20x1=134 mg, s1=3.64 mg, n1=20 
x overbar 2 equals 88 mg comma s 2 equals 2.02 mg comma n 2 equals 16x2=88 mg, s2=2.02 mg, n2=16 

ConfidenceConfidence interval wheninterval when variances arevariances are not equal 
left parenthesis x overbar 1 minus x overbar 2 right parenthesis minus t Subscript c Baseline StartRoot StartFraction s Subscript 1 Superscript 2 Over n 1 EndFraction plus StartFraction s Subscript 2 Superscript 2 Over n 2 EndFraction EndRoot less than mu 1 minus mu 2 less than left parenthesis x overbar 1 minus x overbar 2 right parenthesis plus t Subscript c Baseline StartRoot StartFraction s Subscript 1 Superscript 2 Over n 1 EndFraction plus StartFraction s Subscript 2 Superscript 2 Over n 2 EndFraction EndRootx1−x2−tcs21n1+s22n2<μ1−μ2<x1−x2+tcs21n1+s22n2 

d.f. is the smaller of
n 1n1minus−1 orn 2n2minus−1 
Enter the endpoints of the interval.
nothing less than mu 1 minus mu 2 less than nothing<μ1−μ2<
(Round to the nearest integer as needed.)
Using Two sample t test assuming unequal variance.
Given: = 0.01
Population 1:
n1 = 20, = 134, S1 = 3.64
Population 2:
n2 = 16, = 88, S2 = 2.02
Degrees of Freedom:
Critical value:
…………………..….using t table
99% Confidence Interval:
(43.37, 48.63)
Or
43 < 12 < 49 .........rounded to the nearest integer
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