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

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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

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