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

question 151

Short Answer

SCENARIO 11-10-B
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-DataB.XLSX. $$\begin{array} { l l l l l l l l l l l } \text { Vendor A } & 1460 & 1519 & 1364 & 1521 & 1628 & 1265 & 1552 & 1496 & 1411 & 1614 \\& 1508 & 1587 & 1484 & 1554 & 1459 & 1529 & 1515 & 1446 & 1517 & 1511 \\& 1563 & 1548 & 1536 & 1478 & 1665 & 1656 & 1544 & 1361 & 1573 & 1429 \\\text { Vendor B } & 2941 & 2975 & 3231 & 2890 & 3001 & 2930 & 2924 & 2916 & 3048 & 3066 \\& 3012 & 3108 & 2982 & 3126 & 3105 & 2879 & 2944 & 3066 & 2984 & 3057 \\& 3217 & 3058 & 2987 & 2977 & 3178 & 3252 & 3024 & 3156 & 3029 & 3103 \\\text { Vendor C } & 2020 & 1928 & 2135 & 1777 & 2005 & 2061 & 2029 & 1860 & 1967 & 2099 \\& 2031 & 2188 & 2137 & 1945 & 1952 & 1905 & 2031 & 1853 & 1974 & 2071 \\& 1966 & 2084 & 1998 & 2179 & 1988 & 2002 & 2178 & 1995 & 2076 & 1873\end{array}$$ 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-B, the numerator and denominator degrees of freedom of the
Tukey-Kramer procedure used to determine which of the three means are different are ________
and ________, respectively.

---

Definitions:

Interval

A range of numbers between two set points.

Real Number Line

A one-dimensional line on which every point corresponds to a real number and every real number to a point.

Real Number Line

A line that graphically represents all possible real numbers, where each point on the line corresponds to a unique real number.

Inequality

An inequality is a mathematical statement indicating that two expressions are not equal, represented by symbols such as > (greater than), < (less than), ≥ (greater than or equal to), or ≤ (less than or equal to).