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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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Chapter
Section
BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

Identifying individuals with a high risk of Alzheimer’ disease usually involves a long series of cognitive tests. However, researchers have developed a 7-Minute Screen, which is a quick and easy way to accomplish the same goal. The question is whether the 7-Minute Screen is as effective as the complete series of tests. To address this question, Juin et al. (2008) administered both tests to a group of patients and compared the results. The following data represent results similar to those obtained in the study.

Patient 7-Minute Screen Cognitive Series
A 3 11
B 8 19
C 10 22
D 8 20
E 4 14
F 7 13
G 4 9
H 5 20
I 14 25

a. Compute the Pearson correlation to measure the degree of relationship between the two test scores.

b. Is the correlation statistically significant? Use a two-tailed test with α = .01.

c. What percentage of variance for the cognitive scores is predicted from the 7-Minute Screen scores? (Compute the value of r2.)

a.

To determine
The Pearson correlation of the given data.

Explanation

Given info:

The given data are shown below,

7-minut screen Cognitive series
3 11
8 19
10 22
8 20
4 14
7 13
4 9
5 20
14 25

Calculation:

Formula to calculate the Pearson correlation is,

r=SPSSxSSY (1)

Where co variability of the variable x and y is SP, SSX is the variability of the x variable and SSY is the variability of the y variable.

Mean of the variable X is,

MX=3+8+10+8+4+7+4+5+149=639=7

Thus the mean of the variable X  is 7.

Mean of the variable Y is,

MY=11+19+22+20+14+13+9+20+259=1539=17

Thus the mean of the variable Y  is 17.

For calculating SSx and SP the table is shown below,

Sr

b.

To determine

To explain: The correlation is statistically significant or insignificant using two tail test at 1% level of significance.

c.

To determine
The percentage of variance for the cognitive scores.

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