Chapter 8: Inferences on the Mean and Variance of a Distribution WB8-01: A random sample with n =10 and s = 0.7 is taken from a normal population. Find a 90% confidence interval for oz (10-1)(0:49) 69 2 _ 01 10 WB8-02: The objectives of a study by Kennedy and Bhambhani were to use physiological measurements to determine the test-retest reliability of the Baltimore Therapeutic Equipment- 4,4) Work Simulator during three simulated tasks performed at light, medium, and heavy work intensities, and to examine the criterion validity of these tasks by comparing them to real tasks /6,919 performed in a controlled, laboratory setting. Subjects were 30 healthy men between the ages of 18 and 35. The investigators reported a standard deviation of 0.57 for the variable peak oxygen consumption (L/min) during one of the procedures. Construct a 95% confidence interval for the population variance for the oxygen consumption. 0 2 60 65370 (30 - 1 ) (0 132 49 )WB8-03: Kubic et al. evaluated the hematologic parameters of 11 patients with documented Bordetella pertussis infection. The subjects consisted of 11 infected children aged one month to 4.5 years. The white blood cell (WBC) counts (x109/L) for the subjects were 20.2, 15.4, 8.3, 29.8, 40.9, 19.7, 49.5, 12.1, 32.0, 72.9, and 13.5. Construct a 90% confidence interval for the variance of the WBC counts for this population. 365, 84 25 11-1/( 365, 8425 Tay 8 1 3070 WB8-04: Forced vital capacity determinations were made on 20 healthy adult males. The 18130 sample variance was 1,000,000. Construct 90% confidence intervals for of and or. (207 ) ( 1, 00 0, 00 0) 30 , 1435 6303 18 31 07(6 26187802083 10,170 WB8-05: In a study of myocardial transit times, appearance transit times were obtained on a sample of 30 patients with coronary artery disease. The sample variance was found to be 1.03. Construct 99% confidence intervals for of and o.\fWB8-08: To estimate the average service time at a fast-food restaurant, a random sample of 35 orders were found to take an average of 72.2 seconds to complete, with a standard deviation of 12.8. Assume that service times are normally distributed. Find a 95% confidence interval for the true mean time to complete an order. WB8-09: The population weights of can of pear halves are normally distributed with a standard deviation of 0.6 ounces. A random sample of 15 cans produced a mean of 16.1 ounces. Find a 95% confidence interval for the true mean weight of these canned pear halves. WB8-10: A new system is believed to speed up registration. The old system took an average of 50 minutes per student. Test to see if the new system is faster. Let u = the mean time to register per student with the new system. Assuming the time to register is nearly normal, a random sample is taken with n =12, x = 42 and s = 11.9. At the 0.05 level of significance, what conclusion can be made? What if a = 0.01 instead?WB8-11: We wonder if fuses labeled 25 amps are labeled properly. Let u = mean number of amps to blow. Assuming a normal distribution, a random sample is taken with n = 25, x = 24.2 and s = 1.9. What conclusion can be reached using an alpha of 0.05? WB8-12: A machine is supposed to fill containers with a standard deviation of no more than 0.5 of an ounce. Quality control engineers are concerned that the true variability is actually greater than 0.25 ounces-squared. Assuming the amount of liquid put into these containers is normally distributed, a random sample is taken with n = 20 and s = 0.58. At the 0.05 level of significance, should the engineers be concerned?\f130 0.366 0.?50 (0.596. 0373] Test Null hypothesis Hu', 0' = 056 Alternative hypothesis H1: 02 it 0.56 Test Method Statistic DF P-Vaiue ChiSquare in}? 129 0.012 WEE-15: A large, nationally known brewery located in the midwest has an iconic team of 3 horses which pull an oldfashion beer deiivery wagon. Suppose the standard deviation of the h"tight [in hands} for this particular breed of horses is known to be 1.2 hands. The brew-re\"t wants the appearance of their team to be as consistent in size as possible. 50 their claim the standard deviation of the height of the horses for their team is significantly less than 1'2 hands. To test this claim, a random sample of 12 horses used for the team was taken. The mean was found to be 13.1 hands with a. standard deviation of 0.43 hands. Based on the sarhple data. is there sufcient evidence to support the brewer-V's claim at the 0.05 level of significance? \"1. \"A