# The study was attempting to control for day of the

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The study was attempting to control for day of the week as a blocking variable. The blocking variable produced an F value that was significant at α = .01. Lead times differ by type of valve. The needle and clack valves have the shortest lead times and the butterfly and poppet valves have the longest lead times. A cursory examination of the mean lead times by day of the week indicates that Monday’s and Friday’s produce the longest lead times.

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Case Notes 31 Chapter 12 Foot Locker in the Shoe Mix 1. Has the distribution of shoe sales by Price Category changed from the year 2000 to the year 2001? A chi-square goodness-of-fit test can be used to test this. Let the 2000 distribution be the expected frequencies and the 2001 values be the observed frequencies. Neither MINITAB nor Excel directly computes a chi-square goodness- of-fit test. Utilizing MINITAB’s calculator capability (could have used Excel’s), the following work is obtained. 2000 2001 chi-sq. 115 126 1.05217 The observed chi-square value is 1.85380 38 40 0.10526 37 35 0.10811 Using an α = .05, and df of k -1 = 7, the critical value is: 30 27 0.30000 χ 7,.05 = 14.0671 22 20 0.18182 21 20 0.04762 11 11 0.00000 17 18 0.05882 2 χ = 1.85380 Since the observed chi-square is less than the critical chi-square, the decision is to fail to reject the null hypothesis. There is not enough evidence to declare that the 2001 distribution of shoe sales is any different than the 2000 distribution of shoe sales. Implications to Foot Locker and Nike is that the target market has not changed. This might mean that marketing attempts to change the target market have not been effective. It might also mean that the production schedule for various types of shoes need not change. Demand for shoes at the various price levels remains constant. If the companies desire to sell more high end shoes, they need to make a renewed effort to effect changes in these distributions. This result basically tells them that they are where they were.
Case Notes 32 2. A chi-square test of independence is used to determine if gender is independent of gender. Shown below is MINITAB output for the analysis of this question. Chi-Square Test: Male, Female Expected counts are printed below observed counts Male Female Total U.S. West 29 43 72 41.27 30.73 U.S. South 48 20 68 38.98 29.02 U.S. East 52 61 113 64.77 48.23 U.S. North 28 25 53 30.38 22.62 Europe 78 32 110 63.05 46.95 Australia 47 29 76 43.56 32.44 Total 282 210 492 Chi-Sq = 3.647 + 4.898 + 2.090 + 2.806 + 2.517 + 3.380 + 0.186 + 0.250 + 3.545 + 4.761 + 0.272 + 0.365 = 28.716 DF = 5, P-Value = 0.000 An observed chi-square of 28.716 was obtained with an associated p -value of .000 on this question. This indicates that gender is not independent of location when it comes to the number of formal suggestions. A cursory examination of the observed values reveals that more suggestions were submitted by females than males in the U.S. West and the U.S. East. However, more suggestions were submitted by males than females in all other regions. In the U.S. South and Europe the ratio of formal suggestions of males to females was over two to one. What this result says is when it comes to making suggestions, the regional culture has an impact on who makes the suggestions. Foot Locker might make

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