Question

Assignment 4 Preview 1. Would you expect a positive, negative, or zero correlative between each of the following pairs of variables? a. Heights of mothers and daughters b. Age and reaction time in the adult population c. Natural gas usage and prevailing (outside) temperature d. Reading skill and shoe size in the population of individuals over 18 years old 2. A researcher hypothesized that there is a relationship between self-esteem and social responsibility, which increases with age. The researcher gave self- esteem and social responsibility inventories to two sets of people: a group of 11 high school students and 10 adults. The data collected are given below (SE = self-esteem; SR = social responsibility). Adults High School Students SE 10

Answer 1

1)

a) Positive correlation

b) Negative correlation

c) No correlation

d) No correlation

2)

a)

Adults

The correlation coefficient value is obtained using the formula,

Y = η(ΣΧΥ) - ΣΧΣΥ [n(Σ Χ2) - (ΣΧ)2] [n(ΣΥ2) - (ΣΥ)2]

r = 10(2248) – 114 x 190 [10(1376) - (114)2] [10(3724) - (190)2)

T=0.8786

b)

High school students

From the data values,

	X	Y	X^2	Y^2	XY
	10	21	100	441	210
	12	20	144	400	240
	13	16	169	256	208
	9	18	81	324	162
	11	19	121	361	209
	5	17	25	289	85
	14	19	196	361	266
	6	10	36	100	60
	8	13	64	169	104
	10	20	100	400	200
Sum	98	173	1036	3101	1744

ΣΧ = 98, ΣΥ = 173, Σx2 = 1036, ΣΥ2 = 310 ΣΧΥ = 1744

Y = η(ΣΧΥ) - ΣΧΣΥ [n(Σ Χ2) - (ΣΧ)2] [n(ΣΥ2) - (ΣΥ)2]

T=0.5376

c)

To test the

The critical value for the correlation coefficient for degree of freedom = n-2=10-2=8 and significance level = 0.05 is obtained from critical value table

To = 0.632

For adults,

r=0.8786 >re= 0.632 = Significant correlation

For high school students,

r=0.5376 X =0.632 = No significant correlation

d)

Since there is no significant correlation between SE and SR for high school student we can not conclude that increase in self esteem will increase social responsibility

f)

Scatter Plot SR SE