OPRE 3360 Exam 3 Review Ch. 8, 9, 14 Questions And 100% Correct Marking Scheme 2026

Chapter 8 Interval Estimation 1. A 95% confidence interval estimate for a population mean is constructed using a sample of size 40. The interpretation of this confidence interval estimate is that (A) we are 95% confident that this interval includes the true population mean. (B) out of all the possible samples of size 40, there is a 95% chance that we selected a sample whose interval does include the true population mean. (C) 95% of the next 100 samples of size 40 will include the true population mean. (D) A and B 2. A 99% confidence interval estimate for a population mean is wider than a 90% interval estimate to capture the true mean more often. (A) Ture (B) False 3. A simple random sample of 50 items from a population with the population standard deviation of 6 resulted in a sample mean of 32. Find a 90% confidence interval estimate for the population mean. (A) 32±1.442 (B) 32±2.186 (C) 32±1.396 (D) 32±2.274 4. A simple random sample with n=54 provided a sample mean of 22.5 and a sample standard deviation of 4.4. Develop an 80% confidence interval for a population mean. (A) 22.5±0.770 (B) 22.5±0.508 (C) 22.5±0.760 (D) 22.5±0.777 5. Mileage tests are conducted for a particular model of automobile. If a 98% confidence interval with margin of error of 1 mile per gallon is desired, how many automobiles should be used in the test? Assume that preliminary mileage tests indicate the standard deviation is 2.6 miles per gallon. 6. In June 2014, Pew Research reported that in 16% of all homes with a stay-at-home parent, the father is the stay-athome parent. An independent research firm has been charged with conducting a sample survey to obtain more current information. What sample size is needed if the research form’s goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.03? Use a 95% confidence level. 7. In case of uncertainty about an appropriate planning value of p* , what value of p* should be used in determining the sample size that will be sufficient to obtain the desired margin of error. Explain. Answers Ch. 8: 1. D 2. A 3. C 4. D 5. use n=36 6. use n=574 7. p*=0.5 (provides the largest sample size). Chapter 9 Hypothesis Tests Read Chapter 9 summary, pg. 437-438, know glossary and key formulas (pg.438) Example: The production line for Glow toothpaste is designed to fill tubes with a mean weight of 6 oz. Periodically, a sample of 30 tunes will be selected in order to check the filling process. Quality assurance procedures call for the continuation of the filling process if the sample results are consistent with the assumption that the mean filling weight for the population of toothpaste tubes is 6 oz; otherwise, the process will be adjusted. Assume that a sample of 30 toothpaste tubes provide a sample mean of 6.1 oz. The population standard deviation is believed to be 0.2 oz. Perform a hypothesis test, at the 0.03 level of significance, to help determine whether the filling process should continue operating or be stopped and corrected. Determine which possible error was committed (Type I or Type II). Answer: Ho:μ=6 vsHa:μ≠6.Test Statistic: zSTAT=2.739; p-value=0.0062, Reject Ho in favor of Ha; Conclude that filling processes need to be adjusted. Type I error: Error of concluding that mean weight is different from 6 oz when in fact it is not. Adjusting filling process when it not needed. For each shipment of parts, a manufacturer wants to accept only those shipments with at most 10% defective parts. A large shipment has just arrived. A quality control manager randomly selects 50 of the parts from the shipment and finds that 6 parts are defective. Let mu denote the number of defective parts in the current shipment and let p denote the proportion of defective parts among the current shipment.