Download Statistical Analysis Homework Solutions: Confidence Intervals for Means and Differences - and more Assignments Statistics in PDF only on Docsity! Stat 4706 HW 2 Solutions Total Points Possible: 26 Instructions: Show all work. Calculations of x-bar and s and intermediate calculations may be done with a calculator or software, but do not use any software programs to generate the interval for you. 1) Methyl t-butyl ether (MTBE) is an organic water contaminant that often results from gasoline spills. The level of MTBE is thought to follow a normal distribution. The level of MTBE (in parts per billion) was measured for a sample of 12 well sites located near a gasoline service station in New Jersey, with the following results: 150, 367, 38, 11, 134, 12, 251, 63, 8, 13, 107. a) Find a point estimate for the population mean MTBE level for all well sites located near that NJ gasoline station. b) Calculate a 90% confidence interval for the population mean. c) Calculate a 99% confidence interval for the population mean. What happens to the width of the interval when we increase the confidence level? Worth 2 points Worth 2 points: -1 if formula correct bur answer is wrong Worth 1 point: -1 if relationship between confidence level and interval width is not mentioned d) Suppose we took a new sample of 25 well sites and found a sample mean and standard deviation equal to those for the above sample. Calculate a 90% confidence interval for the population mean using n=25. What happens to the width of the interval when we increase the sample size? 2) The Journal of Environmental Engineering (2/86) reported on a heat transfer model designed to predict winter heat loss in wastewater treatment clarifiers. The analysis involved a comparison of clear-sky solar irradiation for horizontal surfaces at different sites in the Midwest. The day-long solar irradiation levels (in BTU/sq. ft.) at two Midwestern locations of different latitudes (St. Joseph, MO and Iowa Great Lakes) were recorded on each of seven clear-sky winter days. The data are given in the table below. Find a 95% confidence interval for the mean difference between the day-long clear-sky solar irradiation levels at the two sites. Day St. Joseph Iowa Great Lakes Difference Difference-Squared Day 1 782 593 189 35721 Day 2 956 672 284 80656 Day 3 948 750 198 39204 Day 4 1181 988 193 37249 Day 5 1414 1226 188 35344 Day 6 1633 1462 171 29241 Day 7 1852 1698 154 23716 Total 1377 281131 Worth 2 points: -1 if formula correct bur answer is wrong Worth 1 point: -1 if relationship between sample size and interval width is not mentioned
