26 The quality control manager of a tire company wishes to e

26) The quality control manager of a tire company wishes to estimate the tensile strength of a standard size of rubber used to make a class of radial tires. A random sample of 16 pieces of rubber from different production batches is subjected to a stress test. The test measures the force (in pounds) needed to break the rubber. The results were: 238, 244, 221, 219, 222, 231, 242, 229, 230, 245, 256, 211, 220, 205, 250. Determine the 99% confidence interval.

Solution

mean = sum of values /number of values = 229.533

variance = sum of ( values-mean)^2/number of values =193.0489

standard deviation = sqrt(variance) = 13.894

confidence interval = mean +/- z-score * std/sqrt(n)

= 229.533 +/- 2.577 * 13.894/sqrt(16)

= (220.58 , 238.48)