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A leakage test was conducted to determine the
Chapter 7, Problem 10E(choose chapter or problem)
A leakage test was conducted to determine the effectiveness of a seal designed to keep the inside of a plug airtight. An air needle was inserted into the plug, and the plug and needle were placed under water. The pressure was then increased until leakage was observed. Let \(X\) equal the pressure in pounds per square inch. Assume that the distribution of \(X\) is \(N\left(\mu, \sigma^{2}\right)\). The following n = 10 observations of X were obtained:
\(\begin{array}{llllllllll}
3.1 & 3.3 & 4.5 & 2.8 & 3.5 & 3.5 & 3.7 & 4.2 & 3.9 & 3.3
\end{array}\)
Use the observations to
(a) Find a point estimate of \(\mu\).
(b) Find a point estimate of \(\sigma\).
(c) Find a \(95 \%\) one-sided confidence interval for \(\mu\) that provides an upper bound for \(\mu\).
Questions & Answers
QUESTION:
A leakage test was conducted to determine the effectiveness of a seal designed to keep the inside of a plug airtight. An air needle was inserted into the plug, and the plug and needle were placed under water. The pressure was then increased until leakage was observed. Let \(X\) equal the pressure in pounds per square inch. Assume that the distribution of \(X\) is \(N\left(\mu, \sigma^{2}\right)\). The following n = 10 observations of X were obtained:
\(\begin{array}{llllllllll}
3.1 & 3.3 & 4.5 & 2.8 & 3.5 & 3.5 & 3.7 & 4.2 & 3.9 & 3.3
\end{array}\)
Use the observations to
(a) Find a point estimate of \(\mu\).
(b) Find a point estimate of \(\sigma\).
(c) Find a \(95 \%\) one-sided confidence interval for \(\mu\) that provides an upper bound for \(\mu\).
ANSWER:Step 1 of 4
Given:
The distribution of X (pressure in pounds per square inch) is assumed to be normal with parameters \(\mu \) and \({\sigma ^2}\).
The sample size is n = 10.
The following observations of X were obtained:
3.1, 3.3, 4.5, 2.8, 3.5, 3.5, 3.7, 4.2, 3.9, 3.3