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A manufacturer of hard safety hats for construction
Chapter 10, Problem 78E(choose chapter or problem)
A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces its helmets transmit to wearers when subjected to a standard external force. The manufacturer desires the mean force transmitted by helmets to be 800 pounds (or less), well under the legal 1000-pound limit, and desires \(\sigma\) to be less than 40. Tests were run on a random sample of n = 40 helmets, and the sample mean and variance were found to be equal to 825 pounds and \(2350 \text { pounds }^{2}\), respectively.
a If \(\mu=800\) and \(\sigma=40\), is it likely that any helmet subjected to the standard external force will transmit a force to a wearer in excess of 1000 pounds? Explain.
b Do the data provide sufficient evidence to indicate that when subjected to the standard external force, the helmets transmit a mean force exceeding 800 pounds?
c Do the data provide sufficient evidence to indicate that \(\sigma\) exceeds 40?
Questions & Answers
QUESTION:
A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces its helmets transmit to wearers when subjected to a standard external force. The manufacturer desires the mean force transmitted by helmets to be 800 pounds (or less), well under the legal 1000-pound limit, and desires \(\sigma\) to be less than 40. Tests were run on a random sample of n = 40 helmets, and the sample mean and variance were found to be equal to 825 pounds and \(2350 \text { pounds }^{2}\), respectively.
a If \(\mu=800\) and \(\sigma=40\), is it likely that any helmet subjected to the standard external force will transmit a force to a wearer in excess of 1000 pounds? Explain.
b Do the data provide sufficient evidence to indicate that when subjected to the standard external force, the helmets transmit a mean force exceeding 800 pounds?
c Do the data provide sufficient evidence to indicate that \(\sigma\) exceeds 40?
ANSWER:Step 1 of 4
Given data:
A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces its helmets transmit to wearers when subjected to a standard external force. The manufacturer desires the mean force transmitted by helmets to be 800 pounds (or less), well under the legal 1000-pound limit, and desires ? to be less than 40. Tests were run on a random sample of n = 40 helmets, and the mean and variance were equal to 825 pounds and 2350 pounds, respectively.
Let \(\mu\) be the mean force transmitted by helmets to be 800 pounds (or less) \(\mu=800\)
The manufacturer desires \(\sigma<40\).
The sample size is given as n = 40.
The sample mean is given as \(\bar{x}=825\).
Sample variance is given as \(s^{2}=2350\).
Let X be the standard of the helmet.