I. The administrator of a physical therapy facility has found that postoperative performance scores on a knee flexibility test have tended to follow a normal distribution with a standard deviation of 4. For a simple random sample of ten patients who have recently had knee surgery, the scores are as follows: 101, 92, 94, 88, 52, 93, 76, 84, 72, and 98. Construct and interpret the 90% and 95% confidence intervals for the population mean.
II. A simple random sample of 25 has been collected from a normally distributed population for which it is known that s= 17.0. The sample mean has been calculated as 342.0, and the sample standard deviation is s =14.9. Construct and interpret the 95% and 99% confidence intervals for the population mean.
III. Given the following observations in a simple random sample from a population that is approximately normally distributed, construct and interpret the 90% and 95% confidence intervals for the mean: 67 79 71 98 74 70 59 102 92 96
IV. According to Nielsen/NetRatings, the average visitor to amazon.com spends 19.7 minutes at the site. Assuming this finding to be based on a simple random sample of 20 visitors to the site, with a sample standard deviation of s = 4.0 minutes, and from a population that is approximately normally distributed, construct and interpret the 98% confidence interval for the population mean. Given this confidence interval, would it seem very unusual if another sample of this size were to have a mean visiting time of 18.5 minutes?