Business Case # 2

DECSCI2 Business Case # 2 Chi-Squared Tests

A BIPARTISAN AGENDA FOR CHANGE In a study conducted by Zogby International for the Rochester 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. 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, and Republican) of each individual surveyed was recorded, as well as their responses to the following three questions. (All questions are answerable by Yes or No): 1) Should legislative pay be cut for every day the state budget is late? 2) Should there be more restrictions on lobbyists? 3) Should there be term limits requiring that legislators serve a fixed number of years? The responses were coded using 1 for Yes and 2 for No. The complete data is available in the data set named NYReform.xlsx. MANAGERIAL REPORT: 1.) Use descriptive statistics to summarize the data from this study. 2.) With regard to Question (1), test for the independence of the response (Yes or No) and party affiliation. Use 𝛼 = 0.05. 3.) With regard to Question (2), test for the independence of the response (Yes or No) and party affiliation. Use 𝛼 = 0.05. 4.) With regard to Question (3), test for the independence of the response (Yes or No) and party affiliation. Use 𝛼 = 0.05. 5.) Does it appear that there is broad support for change across all political lines? Explain.

   

Let µo = mean distance of current golf ball models   µa = mean distance of new golf ball models

1. Ho : µo - µa = 0 Ha : µo - µa ≠ 0 (two-tailed test) 2. α = 0.05 [σC & σN unknown; pooled t-test] 3. Reject Ho if tstat ≥ tdf,α = t78,0.05 = 1.665 *df = n1 + n2 – 2 = 40 + 40 – 2 = 78 4.

* Population 1 = Current Model Population 2 = New Model

5.

1.328 ≥ 1.665 è Do Not Reject Ho

6. The mean driving distance of the current model golf balls and new model golf balls are not significantly different.

   

Recommendation: From the data above, Par’s new model golf ball does not only have a new coating, which makes it cut-resistant and long lasting, but also offers driving distances comparable to those of the current model golf ball. Par, Inc. can introduce the new golf ball to increase their market share since the new golf ball has an improved coating and is similar to the current model golf ball when it comes to the driving distance.