Mathematical Statistics with Applications
Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Chapter 10.9, Problem 78E

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 σ 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 pounds2, respectively.

  1. a If µ = 800 and σ = 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.
  2. 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?
  3. c Do the data provide sufficient evidence to indicate that σ exceeds 40?
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Chapter 10 Solutions

Mathematical Statistics with Applications

Ch. 10.3 - The output voltage for an electric circuit is...Ch. 10.3 - The Rockwell hardness index for steel is...Ch. 10.3 - Shear strength measurements derived from...Ch. 10.3 - Prob. 22ECh. 10.3 - Studies of the habits of white-tailed deer...Ch. 10.3 - A study by Childrens Hospital in Boston indicates...Ch. 10.3 - An article in American Demographics reports that...Ch. 10.3 - According to the Washington Post, nearly 45% of...Ch. 10.3 - The state of California is working very hard to...Ch. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - In March 2001, a Gallup poll asked. How would you...Ch. 10.3 - A political researcher believes that the fraction...Ch. 10.3 - Exercise 8.58 stated that a random sample of 500...Ch. 10.3 - Michael Sosin investigated determinants that...Ch. 10.3 - Prob. 36ECh. 10.4 - Refer to Exercise 10.19. If the voltage falls as...Ch. 10.4 - Refer to Exercise 10.20. The steel is sufficiently...Ch. 10.4 - Refer to Exercise 10.30. Calculate the value of ...Ch. 10.4 - Refer to Exercise 10.33. The political researcher...Ch. 10.4 - Refer to Exercise 10.34. Using the rejection...Ch. 10.4 - In Exercises 10.34 and 10.41, how large should the...Ch. 10.4 - A random sample of 37 second graders who...Ch. 10.4 - Refer to Exercise 10.43. Find the sample sizes...Ch. 10.5 - Refer to Exercise 10.21. Construct a 99%...Ch. 10.5 - Prob. 46ECh. 10.5 - Prob. 47ECh. 10.5 - Prob. 48ECh. 10.5 - Prob. 49ECh. 10.6 - High airline occupancy rates on scheduled flights...Ch. 10.6 - Two sets of elementary schoolchildren were taught...Ch. 10.6 - A biologist has hypothesized that high...Ch. 10.6 - How would you like to live to be 200 years old?...Ch. 10.6 - Do you believe that an exceptionally high...Ch. 10.6 - A check-cashing service found that approximately...Ch. 10.6 - Prob. 56ECh. 10.6 - Prob. 57ECh. 10.6 - Prob. 58ECh. 10.8 - Why is the Z test usually inappropriate as a test...Ch. 10.8 - Prob. 62ECh. 10.8 - A chemical process has produced, on the average,...Ch. 10.8 - A coin-operated soft-drink machine was designed to...Ch. 10.8 - Operators of gasoline-fueled vehicles complain...Ch. 10.8 - Researchers have shown that cigarette smoking has...Ch. 10.8 - Nutritional information provided by Kentucky Fried...Ch. 10.8 - Prob. 68ECh. 10.8 - Two methods for teaching reading were applied to...Ch. 10.8 - A study was conducted by the Florida Game and Fish...Ch. 10.8 - Under normal conditions, is the average body...Ch. 10.8 - Prob. 72ECh. 10.8 - In Exercise 8.83, we presented some data collected...Ch. 10.8 - Prob. 74ECh. 10.8 - Prob. 75ECh. 10.8 - Prob. 76ECh. 10.8 - Prob. 77ECh. 10.9 - A manufacturer of hard safety hats for...Ch. 10.9 - Prob. 79ECh. 10.9 - Prob. 80ECh. 10.9 - Prob. 81ECh. 10.9 - Exercises 8.83 and 10.73 presented some data...Ch. 10.9 - Prob. 83ECh. 10.9 - An experiment published in The American Biology...Ch. 10.9 - Prob. 85ECh. 10.9 - Aptitude tests should produce scores with a large...Ch. 10.9 - Prob. 87ECh. 10.10 - Refer to Exercise 10.2. Find the power of the test...Ch. 10.10 - Prob. 89ECh. 10.10 - Refer to Exercise 10.5. a Find the power of test 2...Ch. 10.10 - Let Y1, Y2,, Y20 be a random sample of size n = 20...Ch. 10.10 - Consider the situation described in Exercise...Ch. 10.10 - For a normal distribution with mean and variance...Ch. 10.10 - Suppose that Y1, Y2, ,Yn constitute a random...Ch. 10.10 - Prob. 95ECh. 10.10 - Prob. 96ECh. 10.10 - Prob. 97ECh. 10.10 - Prob. 98ECh. 10.10 - Prob. 99ECh. 10.10 - Prob. 100ECh. 10.10 - Prob. 101ECh. 10.10 - Prob. 102ECh. 10.10 - Prob. 103ECh. 10.10 - Refer to the random sample of Exercise 10.103. a...Ch. 10.11 - Let Y1, Y2,, Yn denote a random sample from a...Ch. 10.11 - A survey of voter sentiment was conducted in four...Ch. 10.11 - Prob. 107ECh. 10.11 - Prob. 108ECh. 10.11 - Let X1, X2,, Xm denote a random sample from the...Ch. 10.11 - Show that a likelihood ratio test depends on the...Ch. 10.11 - Suppose that we are interested in testing the...Ch. 10.11 - Prob. 112ECh. 10.11 - Refer to Exercise 10.112. Show that in testing of...Ch. 10.11 - Prob. 114ECh. 10 - True or False. a If the p-value for a test is...Ch. 10 - Prob. 116SECh. 10 - Prob. 117SECh. 10 - Prob. 118SECh. 10 - Prob. 119SECh. 10 - Prob. 120SECh. 10 - Prob. 121SECh. 10 - Prob. 122SECh. 10 - A pharmaceutical manufacturer purchases a...Ch. 10 - Prob. 124SECh. 10 - Prob. 125SECh. 10 - Prob. 126SECh. 10 - Prob. 127SECh. 10 - Prob. 128SECh. 10 - Prob. 129SECh. 10 - Prob. 130SE
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