Question

# A psychologist conducted a survey of the attitude towards the sustainability of American energy consumption with...

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.

 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