Question

A sample of 38 paired observations generates the following data: d−d− = 0.5 and s2DsD2 = 5.0. Assume a normal distribution. (You may find it useful to reference the appropriate table: z table or t table)

a. Construct the 99% confidence interval for the mean difference μ_D. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

b. Using the confidence interval, test whether the mean difference differs from zero.

• There is no evidence that the mean difference differs from zero.

• There is evidence that the mean difference differs from zero.

Answer 1

a)

sample mean 'x̄=	0.500
sample size   n=	38.00
sample std deviation s=	2.236
std error 'sx=s/√n=	0.3627

		for 99% CI; and 37 df, value of t=		2.715
		margin of error E=t*std error    =		0.985
		lower bound=sample mean-E =		-0.48
		Upper bound=sample mean+E =		1.48

from above 99% confidence interval for population mean =(-0.48,1.48)

b)since above interval contains 0.

There is no evidence that the mean difference differs from zero