Question

I have half of the answers, need a few more. Pretty please!

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	38%	35%
Slightly Optimistic	27%	26%
Slightly Pessimistic	17%	23%
Pessimistic	18%	16%

Step 1: H0: Attitudes have not changed over time.

Ha: Attitudes have changed over time.

Step 2: The proportions of respondents with each attitude are different for each category (and equal to the previously accepted values).

Step 3: H0: Optimistic=0.38, Slightly Optimistic=0.27, Slightly Pessimistic=0.17, Pessimistic=0.18

Step 4: Ha: There is some difference amongst the proportions.

Step 5: E(nOptimistic)=144.4

Step 6a: E(nSlightly Optimistic)=102.6

Step 6b of 10 :  Find the value of the test statistic. Round your answer to three decimal places. 9.932

*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 0.05 level of significance. Round your answer to three decimal places.

Answer 1

Solution:

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	144.4	133	0.9000
Slightly Optimistic	102.6	98.8	0.1400
Slightly Pessimistic	64.6	87.4	8.0470
Pessimistic	68.4	60.8	0.8444
		Total	9.9314

Chi square test statistic=(fo-fe)²/fe

                                           = 9.9314

                                            ≈9.932

Degrees of freedom = K-1

                                    =4-1

                                Df =3

Critical values of the test at the 0.05 level of significance is 2.353

The P-Value is .019153.

The result is significant at p < 0.05.

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

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