Question

A psychologist conducted a survey of the attitude towards the sustainability of American energy consumption with 250 randomly selected individuals several years ago. The psychologist believes that these attitudes have changed over time. To test this he randomly selects 250 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 7% 5%

Slightly Optimistic 11% 18%

Slightly Pessimistic 25% 22%

Pessimistic 57% 55%

Step 6 of 10 : Find the value of the test statistic. Round your answer to three decimal places. Answer How to enter your answer

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

Step 8 of 10: Find the critical value of the test at the 0.025 level of significance. Round your answer to three decimal places.

Answer 1

step 6)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	1st	2nd	Total
	Optimistic	15.0	15.0	30
	Slightly Optimistic	36.3	36.3	73
	Slightly Pessimistic	58.8	58.8	118
	Pessimistic	140.0	140.0	280
	total	250	250	500
chi square    χ2	=(Oi-Ei)2/Ei	1st	2nd	Total
	Optimistic	0.417	0.417	0.8333
	Slightly Optimistic	2.112	2.112	4.2241
	Slightly Pessimistic	0.239	0.239	0.4787
	Pessimistic	0.045	0.045	0.0893
	total	2.8127	2.8127	5.6255
test statistic X2=		5.625

step 7 :

degree of freedom(df) =(rows-1)*(columns-1)=

3

step 8:

for 3 df and 0.025 level,critical value χ2=

9.348

fail to reject the null hypothesis