289 Problems 20. A company self-insures its large fleet of cars against collisions. To determine its mean repair cost per collision, it has randomly chosen a sample of 16 accidents. If the average repair cost in these accidents is $2,200 with a sample standard deviation of $800, find a 90 percent confidence interval estimate of the mean cost per collision. 21. A standardized test is given annually to all sixth-grade students in the state of Washington. To determine the average score of students in her district, a school supervisor selects a random sample of 100 students. If the sample mean of these students' scores is 320 and the sample standard deviation is 16, give a 95 percent confidence interval estimate of the average score of students in that supervisor's district. 22. Each of 20 science students independently measured the melting point of lead. The sample mean and sample standard deviation of these measurements were (in degrees centigrade) 330.2 and 15.4, respectively. Construct (a) a 95 percent and (b) a 99 percent confidence interval estimate of the true melting point of lead. 23. A random sample of 300 CitiBank VISA cardholder accounts indicated a sample mean debt of $1,220 with a sample standard deviation of $840. Construct a 95 percent confidence interval estimate of the average debt of all cardholders. 24. In Problem 23, find the smallest value v that "with 90 percent confidence," CC exceeds the average debt per cardholder. 25. Verify the formula given in Table 7.1 for the 100(1– a) percent lower confidence interval for u when o is unknown. 26. The following are the daily number of steps taken by a certain individual in 20 weekdays. 2,100 1,984 2,072 1,898 1,950 1,992 2,096 2,103 2,043 2,218 2,244 2,206 2,210 2,152 1,962 2,007 2,018 2,106 1,938 1,956 Assuming that the daily number of steps is normally distributed, construct (a) a 95 percent and (b) a 99 percent two-sided confidence interval for the mean number of steps. (c) Determine the largest value v that, "with 95 percent confidence," will be less than the mean range. 27. Studies were conducted in Los Angeles to determine the carbon monoxide concentration near freeways. The basic technique used was to capture air samples in special bags and to then determine the carbon monoxide concentration by using a spectrophotometer. The measurements in ppm (parts per million) over a sampled period during the year were 102.2, 98.4, 104.1, 101, 102.2, 100.4, 98.6,