MATH 534 Week 4 Homework Problems

1. Question: A random sample of 100 selected from a population with a standard deviation of 10 yielded a mean = 225. The mean and the standard deviation of the distribution of the sample means are __________. 2. Question: Suppose a random sample of 49 is selected from a population of size N = 500 with a standard deviation of 14. If the sample mean is 125, the 99% confidence interval to estimate the population mean is between ____________. 3. Question: A manufacturer wants to purchase a certain product of foil. The foil is stored on 1534 rolls each containing a varying amount of foil with a standard deviation of 12.5. In order to estimate the total number of foil on all the rolls, the manufacturer randomly selected 200 rolls and measured the number of foil on each roll. The sample mean was 48. Then the 95% confidence interval to estimate the population mean of foil is between _____________. 4. Question: Suppose a researcher is interested in understanding the variation in the price of store brand milk. A random sample of 36 grocery stores selected from a population and the mean price of store brand milk is calculated. The sample mean is $3.13 with a standard deviation of $0.23. Construct a 99% confidence interval to estimate the population mean. 5. Question: Suppose a researcher is interested in understanding the variation in the price of store brand milk. A random sample of 36 grocery stores selected from a population and the mean price of store brand milk is calculated. The sample mean is $3.13 with a population standard deviation of $0.25. Construct a 95% confidence interval to estimate the population mean. 6. Question: The following random sample was selected from a normal distribution: 4.5, 6.4, 2.3, 1.8, 5.3, then the 95% confidence interval to estimate the population mean is between ____________. 7. Question: A researcher is interested in estimating the mean weight of a semi trailer truck to determine the potential load capacity. She takes a random sample of 17 trucks and computes a sample mean of 20,000 pounds with sample standard deviation of 1,500. The 95% confidence interval for the population mean weight of a semi trailer truck is ____________. 8. Question: The weights of aluminum castings produced by a process are normally distributed. A random sample of 5 castings is selected; the sample mean weight is 2.21 pounds; and the sample standard deviation is 0.12 pound. The 98% confidence interval for the population mean casting weight is ____________. 9. Question: A national survey of companies included a question that asked whether the customers like the new flavor of a cola from company A. The sample results of 1000 customers, and 850 of them indicated that they liked the new flavor. The 98% confidence interval on the population proportion of people who like the new flavor is ____________. 10. Question: Construct 90%, 95%, and 99% confidence intervals to estimate μ from the following data. State the point estimate. Assume the data come from a normally distributed population. 11. Question: A large national company is considering negotiating cellular phone rates for its employees. The Human Resource department would like to estimate the proportion of its employee population who own an Apple iPhone. A random sample of size 250 is taken and 40% of the sample own an iPhone. The 90% confidence interval to estimate the population proportion is ____________. 12. Question: A large trucking company wants to estimate the proportion of its tracker truck population with refrigerated carrier capacity. A random sample of 200 tracker trucks is taken and 30% of the sample have refrigerated carrier capacity. The 95% confidence interval to estimate the population proportion is ____________. 13. Question: Suppose you want to estimate the proportion of cars that are sport utility vehicles (SUVs) being driven in Kansas City, Missouri, at rush hour by standing on the corner of I-70 and I-470 and counting SUVs. You believe the figure is no higher than 0.40. If you want the error of the confidence interval to be no greater than .03, how many cars should you randomly sample? Use a 90% level of confidence. 14. Question: Is the environment a major issue with Americans? To answer that question, a researcher conducts a survey of 1255 randomly selected Americans. Suppose 717 of the sampled people replied that the environment is a major issue with them. Construct a 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them. What is the point estimate of this proportion? 15. Question: A researcher wants to determine the sample size necessary to adequately conduct a study to estimate the population mean to within 5 points. The range of population values is 80 and the researcher plans to use a 90% level of confidence. The sample size should be at least ________. 16. Question: An insurance company is interested in conducting a study to estimate the population proportion of teenagers who obtain a driving permit within 1 year of their 16th birthday. A level of confidence of 99% will be used and an error of no more than .04 is desired. There is no knowledge as to what the population proportion will be. The size of sample should be at least ________.