Question

Consider the following data drawn independently from normally distributed populations: (You may find it useful to reference the appropriate table: z table or t table) X1 = 27.1 012 = 89.5 n1 = 25 X2 = 30.3 022 = 92.3 n2 = 31 a. Construct the 90% confidence interval for the difference between the population means. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.) Confidence interval is b. Specify the competing hypotheses in order to determine whether or not the population means differ. HO: 41 - 42 = 0; HA: M1 - 42 + 0 HØ: 41 - 42 = 0; HA: 41 - 42 < 0 HØ: 41 - H2 = 0; HA: 41 - 42 > 0

Answer 1

a)

std error σ1-2=√(σ21/n1+σ22/n2)    =

2.561

Point estimate of differnce '=x1-x2 =	-3.200
for 90 % CI value of z=		1.645
margin of error E=z*std error =	4.212
lower bound=(x1-x2)-E =	-7.41
Upper bound=(x1-x2)+E =	1.01
from above 90% confidence interval for population mean =(-7.41 to 1.01)

b)

Ho: μι - μ2 = 0; HA: μι - μ2 2 0

c)

No, since the confidence interval includes the hypothesized value of O.

d)