Question

The data set for this question set (Tab Q1 in the Excel data file) comes from a research project that tracks the elderly residents in a community to monitor their cognitive function and general health. Based on the literature, education is considered a protective factor against dementia, and memory decline is usually the first sign of dementia. So the researchers would like to know whether education level (measured in number of years of formal schooling) is correlated with memory function (a standardized memory test score) in their sample of elderly residents.

a. Create a scatter plot between the two variables using Excel. Paste the plot here and format it into an APA-styled “figure” (see Assignment Guides for APA format). Be sure to submit the Excel file that you used to create the scatter plot. (2 points)

b. Calculate the mean and standard deviation for the two variables separately.

c. Calculate the Z scores for all the scores of the two variables, separately.

Tips: It may help to prevent error and to increase clarity if the process and/or the answers (z scores) are listed in a table format.

Subject ID	education	memory
1	16	112
2	16	117
3	12	96
4	17	114
5	16	106
6	14	80
7	14	89
8	12	94
9	16	113
10	13	111
11	16	112
12	18	84
13	12	108
14	16	95
15	12	117
16	14	83
17	8	106
18	12	100
19	18	120
20	14	103
21	14	89
22	12	94
23	14	113
24	12	111
25	12	108

Answer 1

The purpose of the research study is to see if there is a correlation between the number of years of education and memory loss.

For the same, the data from 25 participants is collected and is presented in the question. To check for correlation, we have to plot a scatter plot of the data. Since the effect of education on memory is to be checked, the x-axis would be education and the y-axis would be the dependent variable i.e. memory. Hence, we get:

Next we are to calculate mean and standard deviation for each of the columns.

The formula for mean is:

where x_i are the data points in the column and n is the number of data points in the column,

The formula for standard deviation is:

Solving for both the columns, we get:

	education	memory
Mean	14	103
Standard deviation	2.3629	11.7721

Next we calculate z-scores for each value. This is done using the formula:

Solving for each column, we get:

Subject ID	education	memory	z_education	z_memory
1	16	112	0.8464	0.7645
2	16	117	0.8464	1.1893
3	12	96	-0.8464	-0.5946
4	17	114	1.2696	0.9344
5	16	106	0.8464	0.2548
6	14	80	0	-1.9538
7	14	89	0	-1.1893
8	12	94	-0.8464	-0.7645
9	16	113	0.8464	0.8495
10	13	111	-0.4232	0.6796
11	16	112	0.8464	0.7645
12	18	84	1.6928	-1.614
13	12	108	-0.8464	0.4247
14	16	95	0.8464	-0.6796
15	12	117	-0.8464	1.1893
16	14	83	0	-1.6989
17	8	106	-2.5393	0.2548
18	12	100	-0.8464	-0.2548
19	18	120	1.6928	1.4441
20	14	103	0	0
21	14	89	0	-1.1893
22	12	94	-0.8464	-0.7645
23	14	113	0	0.8495
24	12	111	-0.8464	0.6796
25	12	108	-0.8464	0.4247