Question

The table below shows the arm spans (in inches) and the heights (in inches) of 10 randomly selected people.

Arm Span, x	51	52	56	49	54	59	58	55	52	56
Height, y	51	53	54	50	55	57	58	57	52	56

Perform a test, at the 5% level of significance, for the population slope β 1 of the regression line.

H₀:

H_a:

t-Test Statistic (round this value to three decimal places) =

Critical t-Score (t α or t α / 2, use the t-distribution table to find, it should contain three decimal places) =

Conclusion (type R for reject H₀, F for fail to reject H₀):

Answer 1

The Regression Equation of Y on X is

Wher "r" = Correlation Coefficient

= Mean of X

= Mean of Y

= Standard Deviation of X

= Standard Deviation of Y

	X	Y
	51	51	-3.2	-3.3	10.24	10.89
	52	53	-2.2	-1.3	4.84	1.69
	56	54	1.8	-0.3	3.24	0.09
	49	50	-5.2	-4.3	27.04	18.49
	54	55	-0.2	0.7	0.04	0.49
	59	57	4.8	2.7	23.04	7.29
	58	58	3.8	3.7	14.44	13.69
	55	57	0.8	2.7	0.64	7.29
	52	52	-2.2	-2.3	4.84	5.29
	56	56	1.8	1.7	3.24	2.89
TOTAL					91.6000	68.1000
MEAN	54.2000	54.3000
S.D	3.0265	2.6096
r	0.9167

Therefore the Regression Equation of Y on X is

.

Therefore the fitted Regression Equation of Y on X is  

Here 0.7904 is the slope of the Regression Equation of Y on X which is denoted by

Therefore  

We frame the Null Hypothesis

:

To test the we use the t - Statistic

Therefore

Given α = 5% = 0.05

; So, we Reject at 5% Level of Significant

Therefore we conclude that

NOTE: The critical value of t has been extracted from the tabulated value of t; which posted below.