Final answer:
To confirm whether the attitudes towards the sustainability of American energy consumption have changed from the first survey to the second survey, the psychologist can conduct a chi-square test for independence.
Step-by-step explanation:
To confirm whether the attitudes towards the sustainability of American energy consumption have changed from the first survey to the second survey, the psychologist should conduct a hypothesis test. One possible test is the chi-square test for independence. This test can determine if there is a significant association between the two surveys. Here are the steps to perform the test:
- Step 1: Formulate the null and alternate hypotheses. The null hypothesis (H0) states that there is no association between the attitudes in the two surveys. The alternate hypothesis (Ha) states that there is an association between the attitudes in the two surveys.
- Step 2: Select a significance level (alpha) to determine the critical value for the test. Commonly used significance levels are 0.05 or 0.01.
- Step 3: Collect data from the two surveys and organize it into a contingency table.
- Step 4: Calculate the expected frequencies for each cell in the contingency table under the assumption of independence.
- Step 5: Calculate the chi-square test statistic using the formula:
- chi-square = Σ [(observed frequency - expected frequency)² / expected frequency]
- Step 6: Determine the degrees of freedom for the test. The degrees of freedom are calculated as (number of rows - 1) * (number of columns - 1).
- Step 7: Compare the calculated chi-square test statistic with the critical value from the chi-square distribution table. If the calculated chi-square value is greater than the critical value, reject the null hypothesis and conclude that there is an association between the attitudes in the two surveys. Otherwise, fail to reject the null hypothesis.