A psychologist conducted a survey of the attitude towards thesustainability of American energy consumption with 250250 randomlyselected individuals several years ago. The psychologist believesthat these attitudes have changed over time. To test this herandomly selects 250250 individuals and asks them the samequestions. Can the psychologist confirm his theory that theattitudes have changed from the first survey to the secondsurvey?
| Attitude | 1st Survey | 2nd Survey |
|---|
| Optimistic | 6% | 13% |
| Slightly Optimistic | 12% | 17% |
| Slightly Pessimistic | 22% | 12% |
| Pessimistic | 60% | 58% |
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Step 1 of 10:
State the null and alternative hypothesis.
Step 2 of 10:
What does the null hypothesis indicate about the proportions ofrespondents with each attitude?
Step 4 of 10:
Find the expected value for the number of respondents who areoptimistic. Round your answer to two decimal places. E(noptimistic) =
Step 5 of 10:
Find the expected value for the number of respondents who arepessimistic. Round your answer to two decimal places. E(nPessimistic) =
Step 6 of 10:
Find the value of the test statistic. Round your answer to threedecimal places.
Step 7 of 10:
Find the degrees of freedom associated with the test statisticfor this problem.
Step 8 of 10:
Find the critical value of the test at the 0.05 level ofsignificance. Round your answer to three decimal places.
Step 9 of 10:
Make the decision to reject or fail to reject the nullhypothesis at the 0.05 level of significance.
Step 10 of 10:
State the conclusion of the hypothesis test at the 0.05 level ofsignificance.
