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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%

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

Homework Answers

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
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