Question

Two independent samples have been selected, 67 observations from population 1 and 94 observations from population 2. The sample means have been calculated to be x¯1 = 9.9 and x¯2 = 10.2. From previous experience with these populations, it is known that the variances are σ21= 39 and σ22 = 38

(a) σ(x¯1−x¯2).
answer: _____

(b)    Determine the rejection region for the test of H0:(μ1−μ2)=2.94 and Ha:(μ1−μ2)>2.94 . Use α=0.02
z > : _____

(c)    Compute the test statistic.
z=

(d)    Construct a 98 % confidence interval for (μ1−μ2).
≤(μ1−μ2)≤ : ______

Answer 1

a)

(1 - 2) = sqrt [ 21 / n1 + 22 / n2 ]

= sqrt [ 39 / 67 + 38 / 94 ]

= 0.9931

b)

For right tailed test,

Rejection region = Reject H0 if z > 2.054 (Critical value calculated from Z table for 0.02 significance level)

c)

Test statistics z = (1 - 2) - 0 / (1 - 2)

= (9.9 - 10.2 ) / 0.9931

= -0.30

d)

98% Ci is

(1 - 2) - Z/2 * (1 - 2) < 1 - 2 < (1 - 2) + Z/2 * (1 - 2)

( 9.9 - 10.2) - 2.054 * 0.9931 < 1 - 2 < ( 9.9 - 10.2) + 2.054 * 0.9931

-2.34 <  1 - 2 < 1.74

98% CI is ( -2.34 , 1.74 )