H0: µ1 ≤ µ2, a = 0.01
Sample statistics: ẍ1 = 45, s1 = 4.8, n1 = 16 and ẍ2 = 50, s2 = 1.2, n2 = 14
Assume Ơ 2/1 ≠ Ơ 2/2
a) Find the test statistic
b) Find the standardized test statistic
c) Decide whether the standardized test statistic is in the rejection region
d) Decide whether you should reject or fail to reject the null hypothesis
Sample statistics: ẍ1 = 45, s1 = 4.8, n1 = 16 and ẍ2 = 50, s2 = 1.2, n2 = 14
Assume Ơ 2/1 ≠ Ơ 2/2
a) Find the test statistic
b) Find the standardized test statistic
c) Decide whether the standardized test statistic is in the rejection region
d) Decide whether you should reject or fail to reject the null hypothesis
-
a)
standard error of difference of means = sqrt[ s1^2/n1+s2^2/n2]
=sqrt[ 1.44+0.102857] =
Denominator of t = 1.242118
t = (45 - 50) = -5 / 1.242118
t =-4.0254
b)
degrees of freedom = smaller of the sample sizes. (I didn't use the Welch test)
The critical t(14,0.01) =-2.264
c)
test statistic is in the rejection region
d)
reject the null hypothesis
standard error of difference of means = sqrt[ s1^2/n1+s2^2/n2]
=sqrt[ 1.44+0.102857] =
Denominator of t = 1.242118
t = (45 - 50) = -5 / 1.242118
t =-4.0254
b)
degrees of freedom = smaller of the sample sizes. (I didn't use the Welch test)
The critical t(14,0.01) =-2.264
c)
test statistic is in the rejection region
d)
reject the null hypothesis