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

question 87

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, what are the numerator and denominator degrees of freedom for
Levene's test for homogeneity of variances respectively?

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Definitions:

Canopy Layer

The upper layer of vegetation in a forest, formed by the crowns of trees, which significantly affects the ecosystem beneath by intercepting sunlight and rain.

Short-term Atmospheric Conditions

Refers typically to weather patterns and phenomena over a short period, ranging from minutes to days, including temperature, humidity, precipitation, and other meteorological elements.

Temperate Deciduous Forests

Forests located in temperate zones characterized by trees that shed their leaves annually, experiencing four distinct seasons.

Tropical Forests

are dense, warm, and wet forests found near the equator, rich in biodiversity and playing vital roles in global climate regulation.