Question

3. (7pt) Money taken in from parking meters is an important revenue source for most cities. A random sample of the daily intake from 8 parking meters in one particular city was collected, and the results are reported below. The following data come from a population that is normally distributed. 128 132 121 141 119 149 99 106 Parking Fees Collected ($) a. Based on these data, construct a 98% confidence interval for the average amount of money collected by a parking meter in the city (assume all requirements are met). (Show formula, substitution, and result.) b. A city commissioner claims that the city's parking meters should be eliminated, since they bring in less than $100 per day. Does the above confidence interval support or contradict this claim? (Circle the best choice) Support, since $100 Support, since $100 Contradict, since Contradict, since is below the interval is within the interval $100 is within the $100 is below the interval interval

Answer 1

a)

b) Contradict, since $100 is below the interval.

Let ž denotes the sample mean, s denotes the sample standard deviation and n denotes the sample size. Here, c = 124.375, s2 = 282.267857, s = 16.801, n = 8, standard error = 16.801 78 5.939990 5.940 The critical value is tcritical = t 1-0.98 =t0.01,7 2.997952 2.998 At 98 percent confidence level, The margin of error is: ,7 2 S 16.801 16.801 ME *t 1-0.98 * 10.01,7 * 2.998 = 17.808879 x 17.809 ✓n 2 18 a 98 percent confidence interval of population mean u is S =ī + *t 1-0.98 ,7 ✓n 2 = 124.375 + 16.801 * 10.01,7 V8 = 124.375 + 16.801 * 2.998 18 = 124.375 + 17.809 = = (106.566121, 142.183879) ~ (106.57, 142.18)