Exam 8: Estimating Single Population Parameters

An analyst for a financial investment firm recently went through the effort to determine the required sample size for estimating the mean number of transactions per year for the clients of his firm. The calculations, which were based on a 95 percent confidence level and a margin of error of ±3, gave a required sample size of 300. Given this information, the value used for the population standard deviation must have been about 26.5 transactions.

Sampling error is the difference between a statistic computed from a sample and the corresponding parameter computed from the population.

A regional hardware chain is interested in estimating the proportion of their customers who own their own homes. There is some evidence to suggest that the proportion might be around 0.70. Given this, what sample size is required if they wish a 90 percent confidence level with a margin of error of ±.025?

Under what circumstances would you wish to select a pilot sample?

In a recent report to the supply-chain manager in a major electronics company, the report writer stated that with 90 percent confidence, the manufacturing lead time for a critical part is between 3.34 hours and 4.14 hours. Based on this, the sample mean that generated the confidence interval was 3.60.

An emergency room in a hospital wants to determine the sample size needed for estimating their mean number of visits per day. If they want a 99 percent confidence level the correct critical value to use is 2.33.

The following data represent a random sample of bank balances for a population of checking account customers at a large eastern bank. Based on these data, what is the 95 percent confidence interval estimate for the true population mean?

A local pizza company is interested in estimating the percentage of customers who would take advantage of a coupon offer. To do this, they give the coupon out to a random sample of 100 customers. Of these, 45 actually use the coupon. At the 95 percent confidence level it would be appropriate for the manager to conclude that possibly as many as 50 percent of his customers will redeem the coupon.

The Internal Revenue Service (IRS) is interested in estimating the mean amount of money spent on outside tax service by income tax filers filing as single on their individual form. To do this, they have selected a random sample of n = 16 people from this population and surveyed them to determine the sample mean and sample standard deviation. The following information was observed: Given this information, what is the 95 percent confidence interval for the mean dollars spent on outside tax assistance by taxpayers who file as single?

In estimating a population mean, under what conditions would the t-distribution be used?

The following data represent a random sample of bank balances for a population of checking account customers at a large eastern bank. Based on these data, what is the critical value for a 95 percent confidence interval estimate for the true population mean?

The one sure thing that can be said about a point estimate is that it will most likely be subject to sampling error and not equal the parameter.

A study was recently conducted to estimate the mean cholesterol for adult males over the age of 55 years. From a random sample of n = 10 men, the sample mean was found to be 242.6 and the sample standard deviation was 73.33. To find the 95 percent confidence interval estimate for the mean, the correct critical value to use is:

A pilot sample is one that is used when a decision maker wishes to get an advance idea of what the mean of the population might be.