# Solved Assignments in Statistics / Estimation category

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the brand. How many adults must he survey in order to be 90 % confident that his estimate is within six percentage points of the true population percentage? a) Assume that nothing is known about the percentage of adults who have heard of the brand. n=_________ (Round up to the nearest integer.) b) Assume that a recent survey suggests that about 76 % of adults have heard of the brand. n=_______ (Round up to the nearest integer.)
The proportion of public accountants who have changed companies within the last three years is to be estimated within 3%. The 90% level of confidence is to be used. A study conducted several years ago revealed that the percent of public accountants changing companies within three years was 21·(Use Z Distribution Table.) (Round the z-values to 2 decimal places. Round up your answers to the next whole number.) a. To update this study, the files of how many public accountants should be studied? b. How many public accountants should be contacted if no previous estimates of the population proportion are available?
Suppose the U.S. president wants an estimate of the proportion of the population who support his current policy toward revisions in the health care system. The president wants the estimate to be within 0.03 of the true proportion. Assume a 98% level of confidence. The president's political advisors estimated the proportion supporting the current policy to be 0.54. (Use z Distribution Table.) a. How large of a sample is required? (Round the z-values to 2 decimal places. Round up your answer to the next whole number.) b. How large of a sample would be necessary if no estimate were available for the proportion supporting current policy?
Variability in the return of traded security is often thought as a measure of "total risk of the security. A certain portfolio manager will only invest in a security if its population standard deviation of return does not exceed 10% per month. A sample of 18 monthly returns on a particular security yielded a sample deviation of 14.2% per month. Construct a 90% confidence interval estimate for the population variance.
A national bank analysed a random sample of 365 cheque accounts at their Windhoek branch and found that 78 of them were overdrawn. Estimate, with 90% confidence, the proportion of all bank accounts at the Windhoek branch of the bank that were not overdrawn.
A researcher wishes to estimate, with 99% confidence, the population proportion of adults who are confident with their country's banking system. His estimate must be accurate within 2% of the population proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 25% of the respondents said they are confident with their country's banking system.
The thickness of a plastic film (in mm) on a substrate material is thought to be influenced by the temperature at which the coating is applied. A completely randomized experiment is carried out. Eleven substrates are coated at 125$^o$C resulting in a sample mean thickness of $\overline{x}_1=103.5$ mm and a sample standard deviation of $s_1=10.2$ mm. Another 13 substrates are coated at 150$^o$C for which $\overline{x}_2 =99.7$ mm and $s_2 = 20.1$ mm are observed. It was originally suspected that raising the process temperature would reduce mean coating thickness. i) Calculate a 95% confidence interval for the population mean for substrate one. ii) Calculate a 95% confidence interval for the mean difference in the thickness of the two substrates, is the original claim true (assume the variances are statistically equivalent). Interpret the result.
Listed below are the amounts of mercury (in parts per million, or ppm) found in the tuna sushi sampled at different stores. The sample mean is 1.044 ppm and the sample standard deviation is 0.256. Use technology to construct a 90% confidence interval estimate of the mean amount of mercury in the population. 0.79, 0.99, 1.19, 0.68, 0.99, 1.33, 1.34. What is the confidence interval of the mean amount of mercury in the population?
A city built a new parking garage in a business district. For a random sample of 100 days, daily fees collected averaged \$2,000, with a standard deviation of \$500. Construct a 90% confidence interval estimate of the mean daily income this parking garage generates. Show all work.
An insurance company checks police records on 500 randomly selected auto accidents and notes that teenagers were at the wheel in 80 of them. Construct a 95% confidence interval estimate of the proportion of auto accidents that involve teenage drivers. Show all work.