Example 1: Suppose you work for the Department of Natural Resources and you want to estimate the average length of all walleye fingerlings in a fish hatchery pond. You take a random sample of 10 fingerlings and determine that the average length is 7.5 inches and the standard deviation is 2.3 inches. Using a 95% confidence level, find the confidence interval for the average length of the fingerlings.
Example 2: A major metropolitan newspaper selected a simple random sample of 1,600 readers from their list of 100,000 subscribers. They asked whether the paper should increase its coverage of local news. Forty percent of the sample wanted more local news. What is the 99% confidence interval for the proportion of readers who would like more coverage of local news?
Example 3: Suppose we know that the IQ scores of all incoming college freshmen are normally distributed with standard deviation of 15. We have a simple random sample of 100 freshmen, and the mean IQ score for this sample is 120. Find a 90% confidence interval for the mean IQ score for the entire population of incoming college freshmen.
Example 4: A statistician chooses 27 randomly selected dates, and when examining the occupancy records of a particular motel for those dates, finds a standard deviation of 5.86 rooms rented. If the number of rooms rented is normally distributed, find the 95% confidence interval for the population standard deviation of the number of rooms rented.