Complete question :
Assume that both populations are normally distributed. a) Test whether mu 1 not equals mu 2 at the alpha equals 0.05 level of significance for the given sample data. b) Construct a 95% confidence interval about mu 1 minus mu 2. Sample 1 Sample 2 n 19 19 x overbar 16.2 14.1 s 4.5 3.1
Answer:
(-0.445 ; 4.645)
Null:
H0: mu1 - mu2 = 0
H1 : mu1 - mu2 ≠ 0
Step-by-step explanation:
__________Sample 1 ____ Sample 2
n ___________19 _________19
x overbar ____16.2 ________14.1
s __________ 4.5 _________3.1
The confidence interval : (2 independent means)
(x1 - x2) ± Tcritical * √(s1²/n1) + (s2²/n2)
T(1 - α/2), 36 = 2.03
(16.2 - 14.1) ± 2.03 * √(4.5²/19) + (3.1²/19)
2.1 ± 2.545
Lower boundary = (2.1 - 2.545) = - 0.445
Upper boundary = (2.1 + 2.545) = 4.645
(-0.445 ; 4.645)