Question

A psychologist conducted a survey of the attitude towards the sustainability of American energy consumption with 260randomly selected individuals several years ago. The psychologist believes that these attitudes have changed over time. To test this he randomly selects 260 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	38%	33%
Slightly Optimistic	12%	13%
Slightly Pessimistic	11%	15%
Pessimistic	39%	39%

Can you please answer all steps from 1 to 10?

Thanks

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: The attitudes have not changed from the first survey to the second survey.

Alternative hypothesis: The attitudes have changed from the first survey to the second survey.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.

Analyze sample data. Applying the chi-square goodness of fit test to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = k - 1 = 4 - 1
D.F = 3
(E_i) = n * p_i


X² = 4.9430

where DF is the degrees of freedom, k is the number of levels of the categorical variable, n is the number of observations in the sample, E_i is the expected frequency count for level i, O_i is the observed frequency count for level i, and X² is the chi-square test statistic.

The P-value is the probability that a chi-square statistic having 3 degrees of freedom is more extreme than 4.9430.

We use the Chi-Square Distribution Calculator to find P(X² > 4.9430) = 0.176

Interpret results. Since the P-value (0.176) is greater than the significance level (0.05), we failed to reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that the attitudes have changed from the first survey to the second survey.