Question

Subject ID	education	memory
1	16	112
2	18	117
3	14	96
4	20	114
5	16	106
6	14	80
7	14	89
8	12	94
9	18	113
10	13	111
11	17	112
12	18	84
13	12	108
14	16	95
15	12	117
16	14	83
17	8	106
18	12	100
19	21	120
20	15	103

e. Explain the direction and strength of the relationship based on the r. (2 points total: 1 for strength, 1 for direction)

f. What is the proportion of variance shared between the two variables? (That is, how much of the variance in one variable can be predicted by the variance in the other variable?) (2 points total: 1 if the process is correct but the answer is wrong)

g. If the researcher wants to perform a two-tailed hypothesis test using this data set so that she can generalize the relationship between the two variables from the sample to the population, what would be the null and alternative hypothesis? Write the hypotheses in words and in symbol notation. (2 points total: 1 for each hypothesis, .5 for written, .5 for symbol notation)

h. Using SPSS to analyze the same dataset yields a p value of .245. Based on α = .05, what would be the conclusion of the hypothesis test (use wording of “reject the null hypothesis” or “fail to reject the null hypothesis”? How do you know? (1 point total: .5 for conclusion, .5 for rationale)

Answer 1

### By using The Excel:

### By using Excel:

	education(x)	memory(y)	x^2	y^2	xy
	16	112	256	12544	1792
	18	117	324	13689	2106
	14	96	196	9216	1344
	20	114	400	12996	2280
	16	106	256	11236	1696
	14	80	196	6400	1120
	14	89	196	7921	1246
	12	94	144	8836	1128
	18	113	324	12769	2034
	13	111	169	12321	1443
	17	112	289	12544	1904
	18	84	324	7056	1512
	12	108	144	11664	1296
	16	95	256	9025	1520
	12	117	144	13689	1404
	14	83	196	6889	1162
	8	106	64	11236	848
	12	100	144	10000	1200
	21	120	441	14400	2520
	15	103	225	10609	1545
Total	300	2060	4688	215040	31100

e. The correlation coefficient between x and y is given by:

Therefore there is a positive linear relationship between memory and education.

f) The coefficient of determination is:

This indicates that about 7% of the variability in one variable is explained by the other variable.

i.e The two variables shared 7% of the variance.

g) If the researcher want to perform a two-tailed hypothesis test using this data set so that she can generalize the relationship between the two variables from the sample to the population.

The null and alternative hypothesis will be:

Vs

In word,

Null Hypothesis: There is no significant linear relationship between the two variables memory and education.

Alternative Hypothesis:There is a significant linear relationship between the two variables memory and education.

h) Using the same data set yields a p value of .245. Based on α = .05

Since p value is greater than level of significance alpha=0.05, we are unable to reject the null hypothesis at 5% level of significance.

Therefore we conclude that there is no statistically significant linear relationship between the two variables education and memory.