Question

A psychologist noted that people have more difficulty sleeping in a bright room than in a dark room. She measured whether the intensity of the light could predict the time it took a sample of 4 participants to fall asleep. The data for this hypothetical study are listed in the following table. Intensity of Light (in watts) Time It Took to Sleep (in minutes) 10 20 40 17 30 35 Compute an analysis of regression for this hypothetical study. (Round your answers to two decimal places.) Source of df MS Fobt Variation Regression Residual (error) Total Make a decision to retain or reject the null hypothesis. (Assume alpha equal to 0.05.) Retain the null hypothesis. Reject the null hypothesis.

Answer 1

Here we have data :

x	y
5	9
10	17
20	30
40	35

Here we calculate by excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.92
R Square	0.85
Adjusted R Square	0.77
Standard Error	5.69
Observations	4.00
ANOVA
	df	SS	MS	F	Significance F
Regression	1.00	360.11	360.11	11.14	0.08
Residual (error)	2.00	64.64	32.32
Total	3.00	424.75
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	9.48	4.89	1.94	0.19	-11.55	30.51
X Variable 1	0.71	0.21	3.34	0.08	-0.20	1.62

Correct option "B"

Reject the null hypothesis.

(Here we have sufficient evidence to reject the null hypothesis, becouse F_observed value (11.14 ) is grater than F_critical value (0.08))