Question

Case Problem 1 A Bipartisan Agenda for Change In a study conducted by Zogby International for the Democrat and Chronicle, more than 700 New Yorkers were polled to determine whether the New York state government works. Respondents surveyed were asked questions involving pay cuts for state legislators, byists, term limits for legislators, and whether state citizens should be able to put matters directly on the state ballot for a vote. The results regarding several pro- posed reforms had broad support, crossing all demographic and political lines. Suppose that a follow-up survey of 100 individuals who live in the western region of New York was conducted. The party affiliation (Democrat, Independent, Republican) of each individual surveyed was recorded, as well as their responses to the following three questions. 1. Should legislative pay be cut for every day the state budget is late? Yes No 2. Should there be more restrictions on lobbyists? Yes No 3. Should there be term limits requiring that legislators serve a fixed number of years? Yes No

Answer 1

Sol:

Chi square output for each question is shown below:

Chi-Square Test: CUT PAY FOR LATE BUDGET
Observed Frequencies
	Column variable
Row variable	Yes	No	Total
Democrat	22	14	36
Independent	10	9	19
Republican	39	6	45
Total	71	29	100
Expected Frequencies
	Column variable
Row variable	Yes	No	Total
Democrat	25.56	10.44	36
Independent	13.49	5.51	19
Republican	31.95	13.05	45
Total	71	29	100
Data
Level of Significance	0.05
Number of Rows	3
Number of Columns	2
Degrees of Freedom	2
Results
Critical Value	5.991465
Chi-Square Test Statistic	10.18748
p-Value	0.006135
Reject the null hypothesis
Expected frequency assumption
is met.

Chi-Square Test: RESTRICTIONS ON LOBBYISTS?
Observed Frequencies
	Column variable
Row variable	Yes	No	Total
Democrat	21	15	36
Independent	15	4	19
Republican	34	11	45
Total	70	30	100
Expected Frequencies
	Column variable
Row variable	Yes	No	Total
Democrat	25.2	10.8	36
Independent	13.3	5.7	19
Republican	31.5	13.5	45
Total	70	30	100
Data
Level of Significance	0.05
Number of Rows	3
Number of Columns	2
Degrees of Freedom	2
Results
Critical Value	5.991465
Chi-Square Test Statistic	3.71902
p-Value	0.155749
Do not reject the null hypothesis
Expected frequency assumption
is met.

Chi-Square Test: SUPPORT TERM LIMITS?
Observed Frequencies
	Column variable
Row variable	Yes	No	Total
Democrat	17	19	36
Independent	10	9	19
Republican	32	13	45
Total	59	41	100
Expected Frequencies
	Column variable
Row variable	Yes	No	Total
Democrat	21.24	14.76	36
Independent	11.21	7.79	19
Republican	26.55	18.45	45
Total	59	41	100
Data
Level of Significance	0.05
Number of Rows	3
Number of Columns	2
Degrees of Freedom	2
Results
Critical Value	5.991465
Chi-Square Test Statistic	5.11158
p-Value	0.077631
Do not reject the null hypothesis
Expected frequency assumption
is met.

1: "Support Congressional Team Limits?" because for question 3, the test statistic is 5.1 (yellow line).

2. ?² = 10.19, Reject H₀; ?² = 3.72, Fail to Reject H₀; ?² = 5.11, Fail to Reject H₀

3 Since the proportion of each party answering "Yes" for each question is not consistent across all three political parties, it must indicate that support for the reforms is not independent of political party.

4 The best way to compare these charts visually is to break up each political party bar into two pieces, one for "Yes" and one for "No" creating six pieces for each chart. Then compare the size of the corresponding piece on the observed side to its corresponding piece on the expected side. If the corresponding pieces are very different in size, then it indicates the variables are not independent of each other.

5 The distribution is not applicable to any of the three chi-square tests