Solution Found!
A test was conducted to determine whether a wedge on the
Chapter 7, Problem 6E(choose chapter or problem)
A test was conducted to determine whether a wedge on the end of a plug fitting designed to hold a seal onto the plug was doing its job. The data taken were in the form of measurements of the force required to remove a seal from the plug with the wedge in place (say, \(X\)) and the force required without the plug (say, \(Y\)). Assume that the distributions of \(X\) and \(Y\) are \(N\left(\mu_{X}, \sigma^{2}\right)\) and \(N\left(\mu_{Y}, \sigma^{2}\right)\) respectively. Ten independent observations of \(X\) are
\(\begin{array}{llllllllll}
3.26 & 2.26 & 2.62 & 2.62 & 2.36 & 3.00 & 2.62 & 2.40 & 2.30 & 2.40
\end{array}\)
Ten independent observations of \(Y\) are
\(\begin{array}{llllllllll}
1.80 & 1.46 & 1.54 & 1.42 & 1.32 & 1.56 & 1.36 & 1.64 & 2.00 & 1.54
\end{array}\)
(a) Find a \(95 \%\) confidence interval for \(\mu_{X}-\mu_{Y}\).
(b) Construct box-and-whisker diagrams of these data on the same figure.
(c) Is the wedge necessary?
Questions & Answers
QUESTION:
A test was conducted to determine whether a wedge on the end of a plug fitting designed to hold a seal onto the plug was doing its job. The data taken were in the form of measurements of the force required to remove a seal from the plug with the wedge in place (say, \(X\)) and the force required without the plug (say, \(Y\)). Assume that the distributions of \(X\) and \(Y\) are \(N\left(\mu_{X}, \sigma^{2}\right)\) and \(N\left(\mu_{Y}, \sigma^{2}\right)\) respectively. Ten independent observations of \(X\) are
\(\begin{array}{llllllllll}
3.26 & 2.26 & 2.62 & 2.62 & 2.36 & 3.00 & 2.62 & 2.40 & 2.30 & 2.40
\end{array}\)
Ten independent observations of \(Y\) are
\(\begin{array}{llllllllll}
1.80 & 1.46 & 1.54 & 1.42 & 1.32 & 1.56 & 1.36 & 1.64 & 2.00 & 1.54
\end{array}\)
(a) Find a \(95 \%\) confidence interval for \(\mu_{X}-\mu_{Y}\).
(b) Construct box-and-whisker diagrams of these data on the same figure.
(c) Is the wedge necessary?
ANSWER:Step 1 of 5
Given:
The data in the form of measurements of the force required to remove a seal from the plug with the wedge in place (say, X) and the force required without the plug (say, Y) is provided.
The distributions of X and Y are normal.
Mathematically,
\(X \sim N\left(\mu_{X}, \sigma^{2}\right) \text { and } Y \sim N\left(\mu_{Y}, \sigma^{2}\right)\)