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 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 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.

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