Question

A psychologist conducted a survey of the attitude towards the sustainability of American energy consumption with 380 randomly selected individuals several years ago. The psychologist believes that these attitudes have changed over time. To test this he randomly selects 380 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	6%	1%
Slightly Optimistic	29%	30%
Slightly Pessimistic	24%	28%
Pessimistic	41%	41%

Find the value of the test statistic. Round your answer to three decimal places.

Answer 1

Ho: attitudes have not changed from the first survey to the second survey

H1:attitudes have changed from the first survey to the second survey

here as we know that expected value =total respondents*expected propotion

observed value =total respodents*observed proportion

Attitude	expected,e	observed value,o	(fo-fe)²/fe
Optimistic	22.8	3.8	15.83333
Slightly Optimistic	110.2	114	0.131034
Slightly Pessimistic	91.2	106.4	2.533333
Pessimistic	155.8	155.8	0
		total=	18.4977

chi square test statistic = Σ(fo-fe)²/fe = 18.498

Df=k-1 = 4-1 = 3

p-value = 0.000347

since,p-value<α=0.05,reject Ho

so, there is enough evidence to conclude that attitudes have changed from the first survey to the second survey at α=0.05