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 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.

Homework Answers

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

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