Question

1. College students were asked how important a goal it is to them to have a family and about how important a goal it is for them to be highly successful in their work. Each variable was measured on a scale from 1 “not at all important goal” to 10 “very important goal”. The results were as follows:

Student	Family Goal	Work Goal
1	7	5
2	6	4
3	8	2
4	3	9
5	4	1
6	10	3
7	5	4
8	7	3
9	2	7
10	6	9

1. State the null and research hypothesis.
2. Calculate the r value by hand.
3. What is the interpretation of the critical value compared to the observed value at .05 and .01 levels of significance?
4. What is the conclusion for α = .05? Write up the results at p = .05 in APA format.
5. What is the value of r² and what does that number tell us?

Answer 1

Independent variable (X) : Family Goal

Dependent variable (Y): Work Goal

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	7	5	49	25	35
	6	4	36	16	24
	8	2	64	4	16
	3	9	9	81	27
	4	1	16	1	4
	10	3	100	9	30
	5	4	25	16	20
	7	3	49	9	21
	2	7	4	49	14
	6	9	36	81	54
Total	58	47	388	291	245

Sample size: n=10

Now,

The coefficient of correlation is :

Test statistics:

Degree of freedom: df=n-1=8

Critical value using excel function "=TINV(0.05,8)" are: +/- 2.306

Critical value using excel function "=TINV(0.01,8)" are: +/- 3.355

Since test statistics lies between critical values for both level of significance so we fail to reject the null hypothesis at both levels .05 and .01 .

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The p-value using excel function "=TDIST(1.461,8,2)" is 0.1821

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.

The results in APA format is

t(8) = -1.461, p > 0.05

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The r^2 is

It shows that 21.06% of variation in dependent variable is explained by independent variable.