Market researchers know that background music can influence the mood and purchasing behavior of customers. One study in a super market compared three treatments: no music, French accordion music and Italian string music. Under each condition, the researchers recorded the numbers of bottles of French and other wine purchased. Here is the table that summarizes the data:
| |
No Music |
French Music |
Italian Music |
Total |
| French Wine |
30 |
35 |
30 |
95 |
| Other Wine |
10 |
5 |
20 |
35 |
| Total |
40 |
40 |
50 |
130 |
The team wants to determine if there is a difference in proportions of French wine purchased under the influence of different types of music (at significance level of 0.05). You are a member of that research team and you are required to answer the following questions:
1. State the hypothesis
2. Select the correct formula to calculate the overall proportion (P bar) of the groups and also calculate it
3. After calculating the expected frequencies, calculate the Chi square statistic which is equal to:
4. Using the Chi Square table, determine the critical value
5. Based on your answers in 3 and 4 what is your decision and what is your managerial statement?
| A. For Q1 Choice 1 is: Ho: µNo Music = µFrench Music = µItalian Music; H1: µNo Music ?µFrench Music ? µItalian Music |
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| B. For Q1 Choice 2 is: Ho: ?No Music = ?French Music = ?Italian Music ; H1: ?No Music ??French Music ? ?Italian Music |
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| C. For Q1 Choice 3 is: Ho: ?No Music = ?French Music = ?Italian Music ; H1: Not All Proportions Are Same |
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D. For Q2 Choice 1 is:  2.225 (Where 1 = no music, 2 = French Music and 3 = Italian Music) |
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E. For Q2 Choice 2 is:  0.7308 |
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F. For Q2 Choice 3 is: 0.0171 |
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| G. For Q3 Choice 1 is: 4036.937 |
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| H. For Q3 Choice 2 is: (-107.115) |
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| I. For Q3 Choice 3 is: 8.6504 |
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| J. For Q4 Choice 1 is: 5.9915 |
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| K. For Q4 Choice 2 is: 3.8415 |
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| L. For Q4 Choice 3 is: 5.0239 |
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| M. For Q5 Choice 1 is: Reject the null. There is sufficient evidence to conclude that there is difference between the proportions of sale of French wine under the influence of different musics. |
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| N. For Q5 Choice 2 is: Reject the null. There is insufficient evidence to conclude that there is difference between the proportions of sale of French wine under the influence of different musics. |
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| O. For Q5 Choice 3 is: Do Not Reject the null. There is insufficient evidence to conclude that there is difference between the proportions of sale of French wine under the influence of different musics. |
Image text transcribed for accessibility: X1/n1+X2/n2+x3/n3= X1+X2+X3/n1+n2+n3= p1+p2+p3/n1+n2+n3 =