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Confidence Intervals for Bag Weights: A Statistical Guide
Chapter 7, Problem 4E(choose chapter or problem)
Let \(m\) denote the median weight of “80-pound” bags of water softener pellets. Use the following random sample of \(n=14\) weights to find an approximate 95% confidence interval for \(m\):
\(\begin{array}{lllllll} 80.51 & 80.28 & 80.40 & 80.35 & 80.38 & 80.28 & 80.27 \\ 80.16 & 80.59 & 80.56 & 80.32 & 80.27 & 80.53 & 80.32 \end{array}\)
(a) Find a 94.26% confidence interval for \(m\).
(b) The interval \(\left(y_{6}, y_{12}\right)\) could serve as a confidence interval for \(\pi_{0.6}\). What is its confidence coefficient?
Questions & Answers
QUESTION:
Let \(m\) denote the median weight of “80-pound” bags of water softener pellets. Use the following random sample of \(n=14\) weights to find an approximate 95% confidence interval for \(m\):
\(\begin{array}{lllllll} 80.51 & 80.28 & 80.40 & 80.35 & 80.38 & 80.28 & 80.27 \\ 80.16 & 80.59 & 80.56 & 80.32 & 80.27 & 80.53 & 80.32 \end{array}\)
(a) Find a 94.26% confidence interval for \(m\).
(b) The interval \(\left(y_{6}, y_{12}\right)\) could serve as a confidence interval for \(\pi_{0.6}\). What is its confidence coefficient?
ANSWER:Step 1 of 5
Given:
The weights of the bags of the water softener pallets are as given below:
\(\begin{array}{lllllll} 80.51 & 80.28 & 80.40 & 80.35 & 80.38 & 80.28 & 80.27 \\ 80.16 & 80.59 & 80.56 & 80.32 & 80.27 & 80.53 & 80.32 \end{array}\)
The number of observations given is \(n=14\).
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Confidence Intervals for Bag Weights: A Statistical Guide
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Understand the process of determining the 94.26% confidence interval for the median weight of "80-pound" bags of water softener pellets using a standard normal table and specified formulas. Additionally, explore the steps to deduce a confidence level of 90.47%.