Question

Assume that the differences are normally distributed. Complete parts ​(a) through ​(d) below. Observation 1 2 3 4 5 6 7 8 Upper X Subscript i 42.7 51.2 44.4 48.6 50.2 44.9 51.9 43.6 Upper Y Subscript i 46.6 49.6 48.6 52.7 50.6 47.4 52.4 45.7 ​(a) Determine d Subscript i Baseline equals Upper X Subscript i Baseline minus Upper Y Subscript i for each pair of data. compute d and sd test if Ud<0 at the 0.05 level of signifgance what is the pvalue reject or dont reject compute 95% confidence interval

Answer 1

WE HAVE GIVEN TWO SERIES X AND Y

WE HAVE TO APPLY PAIRED T TEST TO CHECK DIFFERNCE OF THEIR MEAN IS ZERO OR NOT

a) series of difference of x and y is -

X	Y	D
42.7	46.6	-3.9
51.2	49.6	1.6
44.4	48.6	-4.2
48.6	52.7	-4.1
50.2	50.6	-0.4
44.9	47.4	-2.5
51.9	52.4	-0.5
43.6	45.7	-2.1

HERE D IS THE SERIES OF THE DIFFERENCE OF X AND Y

---------------TO FIND THE VALUE OF TEST STATISTIC T AND CONFIDENCE INTERVAL WE WILL USE MINITAB-----------

STEPS ARE AS FOLLOWS-

ENTER THE DATA-----STAT----BASIC STATISTIC----PAIRED T TEST------------

THE OUTPUT IS AS FOLLOWS-

HERE P-VALUE=0.015<0.05, WE REJECT THE NULL HYPOTHESIS H₀ AT 5% LEVEL OF SIGNIFICANCE.

ALSO CONFIDENCE INTERVAL IS GIVEN IN THE MINITAB OUTPUT.