Mathematical Statistics with Applications
7th Edition
ISBN: 9781133384380
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
Publisher: Cengage Learning US
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Chapter 10.9, Problem 83E
a.
To determine
Identify the type of rejection region that would be favoured by the manager of the dairy.
b.
To determine
Identify the type of rejection region that would be favoured by a salesperson for Company A.
c.
To determine
Identify the type of rejection region that would be favoured by a salesperson for Company B.
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A bakery is considering buying one of two gas ovens. The bakery requires that the temperature remain constant during a baking operation. A study was conducted to measure the variance in temperature of the ovens during the baking process. The variance in temperature before the thermostat restarted the flame for the Monarch oven was 3.5 for 15 measurements. The variance for the Kraft oven was 4.6 for 24 measurements. Does this information provide sufficient reason to conclude that there is a difference in the variances for the two ovens? Assume measurements are normally distributed and use a 0.02 level of significance.
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Chapter 10 Solutions
Mathematical Statistics with Applications
Ch. 10.2 - Define and for a statistical test of hypotheses.Ch. 10.2 - An experimenter has prepared a drug dosage level...Ch. 10.2 - Refer to Exercise 10.2. a Find the rejection...Ch. 10.2 - Suppose that we wish to test the null hypothesis...Ch. 10.2 - Let Y1 and Y2 be independent and identically...Ch. 10.2 - We are interested in testing whether or not a coin...Ch. 10.2 - True or False Refer to Exercise 10.6. a The level...Ch. 10.2 - A two-stage clinical trial is planned for testing...Ch. 10.3 - A survey published in the American Journal of...Ch. 10.3 - The hourly wages in a particular industry are...
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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- Boxes of Cheer detergent have the following statement: "Individual packages of Cheer may weight slightly more or less than the marked weight. This is due to normal variations incurred with high speed packaging machines. However, each day's production of Cheer will average slightly above the marked weight." Suppose the ratio of the variances of weights of two different sizes of boxes is to be estimated. A sample of 35 "98 oz." packages yielded weights with a sample variance of 1.45 ounces. A sample of 30 "42 oz." packages yielded weights with a sample variance of 1.05 ounces. Find a 95% confidence interval for the true ratio of the variances.arrow_forwardThe records of a casualty insurance company show that, in the past, its clients have had a mean of 1.9 auto accidents per day with a variance of 0.0036. The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0036. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H, and the alternative 00 hypothesis H, that we would use for this test. Ho: 0 H1: 0 Oarrow_forwardA new material is being tested for use in the manufacture of electrical conduit, to determine whether it will reduce the variance in crushing strength over the old material. Crushing strengths are measured for a sample of size 16 of the old material and a sample of size 20 of the new material. If it is shown that the crushing strength with the new material has smaller variance, the new material will be used.arrow_forwardTwo coworkers commute from the same building. They are interested if there is any variation in the time it takes them to drive to work. They each record their times for 20 commutes. The first worker's times have a variance of 12.1. The second worker's times have a variance of 16.9. The first worker thinks that he is more consistent with his commute times. Test the claim at the 10% level. State the null and alternative hypotheses. А. Hoi o? = o3 Hoi o} > o? Họ: o = o3 В. Hoi of < o3 C. Họ: of = o? Hoi of t o?arrow_forwardSuppose you are testing two treatments for an illness, Treatment A and Treatment B. Assume that your populations for Treatments A and B are both normal, and both have variances o?. Treatment A is a new treatment, and Treatment B is the established treatment, The effects of the two treatments are measured on a numerical scale. You want to show that Treatment A is better than Treatment B. Through long experience, you know that the average result of Treatment B gives a numerical score of 70. Moreover you also know that the standard deviation is approximately 2. You make the null hypothesis that uA = 80. (a) Suppose you have 1,000 volunteers for Treatment A and 900 for Treatment B. You take a random sample of size n 100, and you find that for Treatment A you have TA 120. What, if anything, can you conclude? (b) What are the probabilities for Type I and Type II errors under the assumption Ho : HA = 80?arrow_forwardSuppose that in a certain year, it was reported that the variance in GMAT scores was 14,650. At a recent summit, a group of economics professors met to discuss the GMAT performance of undergraduate students majoring in economics. Some expected the variability in GMAT scores achieved by undergraduate economics students to be greater than the variability in GMAT scores of the general population of GMAT takers. However, others took the opposite view. Suppose the following are GMAT scores for 51 randomly selected undergraduate students majoring in economics. 345 749 427 765 336 777 663 451 787 454 711 544 453 330 718 462 585 658 550 576 771 572 629 591 481 574 510 628 532 411 702 640 686 608 510 509 617 576 546 392 512 571 794 690 581 527 329 451 666 377 720 (a) Compute the mean, variance, and standard deviation of the GMAT scores for the 51 observations. (Round your answers to two decimal places.) x=s2=s= (b) Develop hypotheses to test whether…arrow_forwardSuppose that in a certain year, it was reported that the variance in GMAT scores was 14,650. At a recent summit, a group of economics professors met to discuss the GMAT performance of undergraduate students majoring in economics. Some expected the variability in GMAT scores achieved by undergraduate economics students to be greater than the variability in GMAT scores of the general population of GMAT takers. However, others took the opposite view. Suppose the following are GMAT scores for 51 randomly selected undergraduate students majoring in economics. 345 749 427 767 336 777 663 451 787 454 711 544 453 330 718 462 585 658 550 576 773 572 629 591 481 574 510 628 532 411 702 640 686 608 510 509 617 576 546 392 512 573 794 690 581 527 329 451 666 377 720 (a) Compute the mean, variance, and standard deviation of the GMAT scores for the 51 observations. (Round your answers to two decimal places.) x= ( ) s2=( ) s= ( ) (b) Develop hypotheses…arrow_forwardThe accounting department analyzes the variance of the weekly unit costs reported by two production departments. A sample of 16 cost reports for each of the two departments shows cost variances of 2.3 and 5.4, respectively. Is this sample sufficient to conclude that the two production departments differ in terms of unit cost variance? Use a = .10. a. State the null and alternative hypotheses. Ho: 0 12 equal to H : 0 1 ? not equal to 2 b. Calculate the value of the test statistic (to 2 decimals). c. The p-value is between .10 and .20 v d. What is your conclusion? Cannot conclude that the departments differ in terms of unit cost variance varrow_forwardThe records of a casualty insurance company show that, in the past, it’s clients have had a mean of 1.8 auto accidents per day with a variance of 0.0025. The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0025. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries claim. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test.arrow_forwardarrow_back_iosarrow_forward_ios
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