Question

6. A social scientist in Austin sees 470 people waiting in line for breakfast tacos at Jo’s on South Congress Ave. Strolling along the sidewalk with her clipboard, she asks each of them two questions. First, “Do you consider yourself more liberal or more conservative?” Second, “Neighborhood gentrification occurs when more affluent people move in to poorer neighborhoods, bringing fancy shops and restaurants and higher real estate prices. Do you think gentrification is mostly good urban revitalization or mostly bad long time resident displacement?”

Revitalization: 141(Conservative) 47(liberal)

Displacement: 39 (conservative) 243(liberal)

A. State appropriate null and alternative hypotheses. (6 points)

B. What is the critical value at the .01 level of significance? (4 points)

C. Calculate the test statistic. Keep things tidy and label steps clearly so that your grader can figure out what you’re doing. (10 points)

D. Give a proper English statement of your conclusion and what your conclusion means in terms of error(s) risked and hypotheses rejected or not. Make reference to the particulars of this problem (political orientation, views of gentrification). (10 points)

Answer 1

A. State appropriate null and alternative hypotheses. (6 points)

The hypothesis being tested is:

H0: Political orientation and views of gentrification are independent

Ha: Political orientation and views of gentrification are not independent

B. What is the critical value at the .01 level of significance? (4 points)

6.635

C. Calculate the test statistic. Keep things tidy and label steps clearly so that your grader can figure out what you’re doing. (10 points)

178.61

D. Give a proper English statement of your conclusion and what your conclusion means in terms of error(s) risked and hypotheses rejected or not. Make reference to the particulars of this problem (political orientation, views of gentrification). (10 points)

Since 178.61 > 6.635, we can reject the null hypothesis.

Therefore, we can conclude that political orientation and views of gentrification are not independent.

		Col 1	Col 2	Total
Row 1	Observed	141	47	188
	Expected	72.00	116.00	188.00
	O - E	69.00	-69.00	0.00
	(O - E)² / E	66.13	41.04	107.17
Row 2	Observed	39	243	282
	Expected	108.00	174.00	282.00
	O - E	-69.00	69.00	0.00
	(O - E)² / E	44.08	27.36	71.45
Total	Observed	180	290	470
	Expected	180.00	290.00	470.00
	O - E	0.00	0.00	0.00
	(O - E)² / E	110.21	68.41	178.61
		178.61	chi-square
		1	df
		9.73E-41	p-value

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