A Bipartisan Agenda for Change As an analyst for the Greater New York Chamber of

Question

A Bipartisan Agenda for Change

As an analyst for the Greater New York Chamber of Commerce, it is your job to analyze voter sentiment in the state so the Chamber can craft policy documents. In a recent 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, restrictions on lobbyists, 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 proposed reforms had broad support, crossing all demographic and political lines.

You decide to conduct a follow-up survey of 100 individuals who live in the western region of New York. The party affiliation (Democrat, Independent, Republican) of each individual surveyed was recorded, as well as their responses to the following 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)

Your first step was to create summary statistics and a graph for each question.

1)Which survey question's chi-square test matches the chi-square distribution below? (Note: The dark blue area is the rejection region of the distribution and the yellow line is the chi-square test statistic.)

a) question 3: "Support Congressional Team Limits?"

b) Question 1: "Cut Legislator Pay for Late Budget?"

c) Question 2: "Restrictions on Lobbyists?"

To confirm or reject your preliminary conclusions based on a visual analysis of all three datasets, you must now compute a chi-square test statistic for each of the three questions in the survey. In each of the tables below, the final column is blank. You must compute the values for the last column and then compute the overall chi-square statistic. The critical value for this test with = 0.05 and df = 2 is 5.99. You must then decide in each case if you will fail to reject the null hypothesis or reject the null hypothesis.

Cut Legislator Pay for Late Budget?

Restrictions on Lobbyists?

Support Congressional Term Limits?

2) Which set of outcomes, in the same order as the charts above and with a critical 2 = 5.99, is correct?

A) 2 = 1.70, Fail to Reject H0; 2 = 0.62, Fail to Reject H0; 2 = 0.85, Fail to Reject H0

B) 2 = 1.70, Reject H0; 2 = 0.62, Fail to Reject H0; 2 = 0.85, Fail to Reject H0

C) 2 = 10.19, Reject H0; 2 = 3.72, Fail to Reject H0; 2 = 5.11, Fail to Reject H0

3) Based on the summary tables and proportional bar charts, you must now make preliminary conclusions about the independence of the response (Yes / No) and party affiliation (Democrat, Independent, Republican) for each question. Which statement represents the best way to interpret the data to make your preliminary conclusion?

A) Since all three political parties seemed to answer "Yes" more than "No" for all but one question/party combination, it means that answering "Yes" is independent of political party.

B) 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.

C) Since the total number of respondents are the same and the height of the bars are the same, I would conclude that the Yes/No response is consistent across all political parties.

While making preliminary conclusions based on graphs may be a good start, you recognize that a quantitative test exists called the chi-square test of independence that will allow you to make a more definitive conclusion.

The first step in conducting a chi-square test is to calculate the frequencies you would expect if the proportions in all groups were equal. The hypothesis is stated as such:

Assuming H0 is true, the expected frequencies for each Yes/No response and political party combination can be calculated using the following expression:

The observed frequency table, the expected frequency table, and each table's proportional bar chart for the first survey question are shown below.

4)You are now given the task of presenting the observed and expected proportional bar charts to your colleagues at the Chamber of Commerce. Which explanation below is the best?

A)The best way to compare these charts visually is to examine the total height of each political party bar. Then compare the height of the corresponding bar on the observed side to the corresponding bar on the expected side. If the corresponding bars are very different in size, then it indicates the variables are not independent of each other.

B)The best way to compare these charts visually is to examine the total height of each political party bar. Then compare the height of the corresponding bar on the observed side to the corresponding bar on the expected side. If the corresponding bars are very different in size, then it indicates the variables are independent of each other.

C)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) Which survey question's chi-square test matches the chi-square distribution below? (Note: The dark blue area is the rejection region of the distribution and the yellow line is the chi-square test statistic.)

A) Question 1: "Cut Legislator Pay for Late Budget?"

B) The distribution is not applicable to any of the three chi-square tests.

C) Question 2: "Restrictions on Lobbyists?"

Yes No Totals Democrat 22 14 36 Independent 10 9 19 Republican 39 6 45 Totals 71 29 00 Yes, No Totals Democrat 21 15 36 Independent 15 4 19 Republican 34 11 45 Totals 70 30 100 Yes No Totals Democrat 17 19 36 Independent 10 9 19 Republican 32 13 45 Totals 59 41 00 30% 20% 10% 20% 100% 30% 20% 10% CUT PAY FOR LATE BUDGET? Democrat Independent Republican Yes No RESTRICTIONS ON LOBBYISTS? Democrat Independent Republican Yes No SUPPORTTERM LIMITS? Democrat Independent Republican Yes No

Explanation / Answer

Chi square output for each question is shown below:

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

#2: Correct option is C) ?2 = 10.19, Reject H0; ?2 = 3.72, Fail to Reject H0; ?2 = 5.11, Fail to Reject H0

#3 Correct option is B) 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 D) 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 Correct option is B) The distribution is not applicable to any of the three chi-square tests.

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.

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