Question

The following table contains information on matched sample values whose differences are normally distributed. Use Table 2.

Number	Sample 1	Sample 2
1	19	22
2	12	11
3	22	21
4	20	22
5	18	20
6	14	19
7	18	19
8	16	20

a.	Construct the 95% confidence interval for the mean difference μD. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.)

Confidence interval is  to

b.	Specify the competing hypotheses in order to test whether the mean difference differs from zero.
	H0: μD ≥ 0; HA: μD < 0 H0: μD = 0; HA: μD ≠ 0 H0: μD ≤ 0; HA: μD > 0

c.	Using the confidence interval from part a, are you able to reject H0?
	No Yes

Answer 1

The table given below ,

Number	Sample 1(X)	Sample 2(Y)	di=X-Y	di^2
1	19	22	-3	9
2	12	11	1	1
3	22	21	1	1
4	20	22	-2	4
5	18	20	-2	4
6	14	19	-5	25
7	18	19	-1	1
8	16	20	-4	16
		Total	-15	61

From table ,

Critical value : ; From excel "=TINV(0.05,7)'

a. The 95% confidence interval for the mean difference μ_{D is ,}

b. Hypothesis : H₀: μ_D = 0; H_A: μ_D ≠ 0

c. Here , the value μ_D = 0 does not lies in the 95% confidence interval.

Therefore , reject H0