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?

A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects. After treatment with the drug, 12 subjects had a mean wake time of 95.6 min and a standard deviation of 42.1 min. Assume that the 12 sample values appear to be from a normally distributed population and construct a 90% confidence interval estimate to the standard deviation of the wake times for a population with the drug treatments. Does the result indicate whether the treatment is effective?

A doctor wants to know if a blood pressure medication is effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects have their blood pressure recorded again. For this test, only systolic pressure is of concern. Test at the 1% significance level. Patient A B C D E F
Before 161 162 165 162 166 171
After 158 159 166 160 167 169

Two types of phone operating system are being tested to determine if there is a difference in the proportions of system failures (crashes). Fifteen out of a random sample of 150 phones with OS1 had system failures within the first eight hours of operation. Nine out of another random sample of 150 phones with OS2 had system failures within the first eight hours of operation. OS2 is believed to be more stable (have fewer crashes) than OS1. Test appropriate hypothesis.

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.

According to the National Traffic Safety Council of Namibia, the probability that a traffic fatality will involve an intoxicated or alcohol-impaired driver is 40%. If eight traffic fatalities observed last month. a. Find the probability that the number of an intoxicated or alcohol-impaired driver is exactly three.
b. Find the expected value and standard deviation of the number of intoxicated or alcohol-impaired drivers.

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.