12 Chapter Tests of Goodness of Fit and Independence
Chapter 12 Tests of Goodness of Fit and Independence Case Problem:
A Bipartisan Agenda for Change
1. Descriptive statistics Question: Should legislative pay be cut for every day the state budget is late?
Yes 22 10 39 71 No 14 9 6 29 Totals 36 19 45 100 Democrat Independent Republican Totals Percentage responding yes: Democrat, 61.1%; Independent, 52.6%; Republican, 86.7%
Preliminary conclusion: Since the percentage of Republicans that answered yes is much greater than the percentage of Democrats or Independents that answered yes, the classifications do not appear to be independent.
Question: Should there be restrictions on lobbyists?
Yes 21 15 34 70 No 15 4 11 30 Totals 36 19 45 100 Democrat Independent Republican Totals Percentage responding yes: Democrat, 58.3%; Independent, 78.9%; Republican, 75.6% Preliminary conclusion: Since the percentage of Democrats that answered yes is much less than the percentage of Independents or Republicans that answered yes, the classifications do not appear to be independent.
Question: Should there be term limits requiring legislators serve a fixed number of years? Yes 17 10 32 59 No 19 9 13 41 Totals 36 19 45 100 Democrat Independent Republican Totals Percentage responding yes: Democrat, 47.2%; Independent, 52.6%; Republican, 71.1% Preliminary conclusion: Since the percentage of Republicans answered that yes is much higher than the percentage of Democrats or Independents that answered yes, the classifications do not appear to be independent. 2. The p-value associated with the test for independence is .006. Since the p-value is less than the level of significance, .05, we can reject the null hypothesis of independence. CP - 33
Chapter 12 Tests of Goodness of Fit and Independence 3. The p-value associated with the test for independence is .156. Since the p-value is greater than the level of significance, .05, we cannot reject the null...