Large Sample Estimation of a Population Mean: Confidence interval for a population mean 1. A government agency was charged by the legislature with estimating the length of time it takes citizens to fill out various forms. Two hundred randomly selected adults were timed as they filled out a particular form. The times required had mean 12.8 minutes with standard deviation 1.7 minutes. Construct a 90% confidence interval for the mean time taken for all adults to fill out this form. 2. Four hundred randomly selected working adults in a certain state, including those who worked at home, were asked the distance from their home to their workplace. The average distance was 8.84 miles with standard deviation 2.70 miles . Construct a 99% confidence interval for the mean distance from home to work for all residents of this state. 3. In order to estimate the mean amount of damage sustained by vehicles when a deer is struck, an insurance company examined the records of 50 such occurrences, and obtained a sample mean of $2,785 with sample standard deviation $221. Construct a 95% confidence interval for the mean amount of damage in all such accidents. 4. For each of 40 high school students in one county the number of days absent from school in the previous year were counted, with the results shown in the frequency table. Construct a 90% confidence interval for the average number of days absent from school of all students in the county. X 0 |1 2 3 4 5 f 24 7 15 2 1 5. A town council commissioned a random sample of 85 households to estimate the number of four-wheel vehicles per household in the town. The results are shown in the following frequency table. Construct a 98% confidence interval for the average number of four-wheel vehicles per household in the town. X 0 1 2 3 4 5 1 16 28 22 12 6