Question

A psychologist conducted a survey of the attitude towards the sustainability of American energy consumption with 230 randomly selected individuals several years ago. The psychologist believes that these attitudes have changed over time. To test this he randomly selects 230 individuals and asks them the same questions. Can the psychologist confirm his theory that the attitudes have changed from the first survey to the second survey? Attitude 1st Survey 2nd Survey Optimistic 35%, 38% Slightly Optimistic 12%, 14% Slightly Pessimistic 9% ,4% Pessimistic 44% ,44%

Step 7 of 10 : Find the degrees of freedom associated with the test statistic for this problem.

Answer 1

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Optimistic	0.350	87.4	80.50	0.77	0.591
Slightly Optimistic	0.120	32.2	27.60	0.88	0.767
Slightly Pessimistic	0.090	9.2	20.70	-2.53	6.389
Pessimistic	0.440	101.2	101.20	0.00	0.000
total	1.000	230	230		7.7470
test statistic X2 =		7.7470
p value =		0.0515

Step 7 of 10 :

degree of freedom =categories-1=

3