Question

A social psychologist hypothesizes that the more initial attraction a person has to another predicts more anxiety before their first date. Below are the first date data from a sample of participants. What can the psychologist conclude with an α of 0.01?

Attraction	Anxiety
2 6 1 3 6 9 6 6 3	8 11 5 8 10 11 8 8 7

a) What is the appropriate statistic?
Slope

Chi-Square

Compute the statistic selected above:

Answer 1

Appropriate statistic- slope

X	Y	XY	X²	Y²
2	8	16	4	64
6	11	66	36	121
1	5	5	1	25
3	8	24	9	64
6	10	60	36	100
9	11	99	81	121
6	8	48	36	64
6	8	48	36	64
3	7	21	9	49
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
42	76	387	248	672

Sample size, n =	9
x̅ = Ʃx/n = 42/9 =	4.66666667
y̅ = Ʃy/n = 76/9 =	8.44444444
SSxx = Ʃx² - (Ʃx)²/n = 248 - (42)²/9 =	52
SSyy = Ʃy² - (Ʃy)²/n = 672 - (76)²/9 =	30.2222222
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 387 - (42)(76)/9 =	32.3333333

Slope, b = SSxy/SSxx = 32.33333/52 = 0.6217949

y-intercept, a = y̅ -b* x̅ = 8.44444 - (0.62179)*4.66667 = 5.542735

Regression equation :

ŷ = 5.5427 + (0.6218) x

Sum of Square error, SSE = SSyy -SSxy²/SSxx = 30.22222 - (32.33333)²/52 = 10.1175214

Standard error, se = √(SSE/(n-2)) = √(10.11752/(9-2)) = 1.20223

Standard error for slope, se(b1) = se/√SSxx = 1.20223/√52 = 0.16672

Slope Hypothesis test:

Null and alternative hypothesis:

Ho: β₁ = 0 ; Ha: β₁ > 0

Test statistic:

t = b/(se_b1) = 3.7296

df = n-2 = 7

p-value = T.DIST.2T(ABS(3.7296), 7) = 0.0037

Conclusion:

p-value < α Reject the null hypothesis.

There is enough evidence to conclude that there is a positive relationship between the two variables.