SCENARIO 11-10-A
You Are the Quality Control Manager of a Water

question 32

Short Answer

SCENARIO 11-10-A
You are the quality control manager of a water bottles company. One of the biggest complaints in the
past years has been the breakage and, hence, the concern on the durability of the connector between
the lid and the bottle which many users use as a handle for the bottles. You have started looking for
alternative replacement for the existing connector design. Three different vendors have proposed
different designs and provided data they have collected on their designs that have been subjected to a
durability test. The data on the number of times the connectors designed by them have been used to
lift the bottles before they break from random samples of 30 bottles are shown below and also
contained in the file Scenario11-10-DataA.XLSX. $$\begin{array} { l l l l l l l l l l l } \text { Vendor A } & 1498 & 1667 & 1530 & 1458 & 1315 & 1458 & 1411 & 1348 & 1583 & 1565 \\& 1495 & 1533 & 1473 & 1654 & 1499 & 1349 & 1486 & 1739 & 1820 & 1543 \\& 1440 & 1652 & 1610 & 1660 & 1563 & 1507 & 1450 & 1501 & 1515 & 1501 \\\text { Vendor B } & 2027 & 2007 & 1977 & 1787 & 2046 & 1945 & 1898 & 2130 & 2096 & 1876 \\& 2014 & 1815 & 1982 & 2004 & 1918 & 1904 & 2061 & 1986 & 1952 & 2061 \\& 2038 & 2227 & 2030 & 2079 & 1884 & 2045 & 2009 & 1970 & 1946 & 2011 \\\text { Vendor C } & 2784 & 3151 & 3126 & 2875 & 2881 & 3000 & 2872 & 3097 & 3020 & 3077 \\& 3082 & 2931 & 2922 & 2877 & 2905 & 3079 & 2916 & 2917 & 3110 & 3121 \\& 3084 & 3065 & 2974 & 2900 & 2860 & 2989 & 2978 & 2881 & 3095 & 2893\end{array}$$ Assume that and the number of times the connectors have been used to lift the bottles before they
break follows a normal distribution. You want to test to see if there is enough evidence of a difference
in mean number of times the connectors have been used to lift the bottles before they break across the
three vendors.
-Referring to Scenario 11-10-A, if a level of significance of 0.05 is chosen for the Tukey-Kramer procedure, which of the following is the correct conclusion on the order of the
Means from the three designs? a) $\mu _ { A } > \mu _ { B } > \mu _ { C }$
b) $\mu _ { C } > \mu _ { B } > \mu _ { A }$
c) $\mu _ { B } > \mu _ { A } > \mu _ { C }$
d) $\mu _ { C } > \mu _ { A } > \mu _ { B }$

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