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%	6%
Slightly Optimistic	9%	6%
Slightly Pessimistic	31%	37%
Pessimistic	53%	51%

Copy Data

Step 6 of 10 :  

Find the value of the test statistic. Round your answer to three decimal places.

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 survey	2nd survey	Total
	Optimistic	16.2500	16.2500	33
	Slightly optimistic	18.7500	18.7500	38
	Slightly Pessimistic	85.0000	85.0000	170
	Pessimistic	130.0000	130.0000	260
	total	250	250	500
chi square    χ2	=(Oi-Ei)2/Ei	1st survey	2nd survey	Total
	Optimistic	0.096	0.096	0.1923
	Slightly optimistic	0.750	0.750	1.5000
	Slightly Pessimistic	0.662	0.662	1.3235
	Pessimistic	0.048	0.048	0.0962
	total	1.5560	1.5560	3.1120
test statistic X2=		3.112

Step 7 of 10:

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

3

step 8 of 10:

for 3 df and 0.025 level,critical value χ2=

9.348