Question

For the data set below, calculate r, r ², and a 95% confidence interval in r units. Then write a one- to two-sentence conclusion statement that includes whether the null hypothesis was rejected or not. Assume a two-tailed hypothesis and α = .05.

	Case 1	Case 2	Case 3	Case 4	Case 5	Case 6
X	1.05	1.15	1.30	2.00	1.75	1.00
Y	2	2	3	4	5	2

Answer 1

sample correlation co-efficient, r = Covariance (X,Y) / = SSxy /

=( Xi)/n = 8.25 / 6 = 1.375

=( Yi)/n = 18 /6 =3

SSxx= (Xi-)2 =(Xi2)-n.2 = 0.83375

SSyy= (Yi-)2 =(Yi2)-n.2 = 8

SSxy= (Xi-)(Yi-) =(XiYi)-n. = 27.05 - 6 * 1.375 * 3 = 2.3

So , r = 2.3 /    = 0.89

• Co-efficient of determination = = 0.89*0.89= 0.79

Standard error of r, SE (r) = = = 0.228

t/2=0.025,4 = 2.776

95% confidence interval for correlation coefficient is

r - t/2=0.025,4 * SE (r) , r + t/2=0.025,4 * SE (r)

= .89 - 2.776 * .228 , .89 + 2.776 * .228

=0.267 , 1.522

But corellation coefficient is always less than equal to 1.

So, 95% confidence interval for correlation coefficient is [0.267 , 1 ]

H0: true correlation co-efficient =0

Ha: true correlation co-efficient 0

Since the confidence interval does not contain 0, we reject null hypothesis.

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