Exam 8: Estimating Single Population Parameters

The national sales manager for a textbook publishing company wishes to estimate the mean number of books sold per college.She wishes to have her estimate be within ± 30 copies and wants a 95 percent confidence interval estimate.If a pilot sample of 30 schools gave a sample standard deviation equal to 60 books,the required total sample size is less than the pilot sample already taken.

In developing a confidence interval estimate,the margin of error is directly dependent on the value of the point estimate.

The product manager for a large retail store has recently stated that she estimates that the average purchase per visit for the store's customers is between $33.00 and $65.00.The $33.00 and the $65.00 are considered point estimates for the true population mean.

A random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph.From past information,it is known that the standard deviation of the population is 22 mph.The 95 percent confidence interval for μ is determined as (61.08,68.92).If we are to reduce the sample size to 100 (other factors remain unchanged),the 95 percent confidence interval for μ would

A random sample of 100 boxes of cereal had a sample mean weight of 396 grams.The standard deviation is known to be 5 grams.The upper end of the confidence interval for the mean is 405.8 grams.

Two confidence interval estimates were developed from the same sample of a population.The wider interval will be the one that has the highest confidence level.

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.

The bottlers of a new fruit juice daily select a random sample of 12 bottles of the drink to estimate the mean quantity of juice in the bottles filled that day.On one such day,the following results were observed: = 12.03; s = 0.12.Based on this information,the margin of error associated with a 90 percent confidence interval estimate for the population mean is 1.7959 ounces.

In estimating a population mean,a large sample size is generally preferable to a small sample size because the margin of error is generally smaller.

When small samples are used to estimate a population mean,in cases where the population standard deviation is unknown:

When developing a confidence interval estimate,the confidence level is calculated based on the size of the sample and the population standard deviation.

To construct a 99 percent confidence interval where σ is known,the correct critical value is 1.96.

An animal shelter wants to estimate the mean number of animals housed daily and they know the standard deviation.If they want to find a 98 percent confidence interval the critical value to use is:

The Hilbert Drug Store owner plans to survey a random sample of his customers with the objective of estimating the mean dollars spent on pharmaceutical products during the past three months.He has assumed that the population standard deviation is known to be $15.50.Given this information,what would be the required sample size to estimate the population mean with 95 percent confidence and a margin of error of ± $2.00?

One factor that plays an important part in determining what the needed sample size is when developing a confidence interval estimate is the level of confidence that you wish to use.

If a population is skewed,the point estimate will be pushed to the right or left of the middle of the confidence interval estimate.

A 95 percent confidence interval estimate indicates that there is a 95 percent chance that the true population value will fall within the range defined by the upper and lower limits.

In estimating a population mean,increasing the confidence level will result in a higher margin of error for a given sample size.

In an application to estimate the mean number of miles that downtown employees commute to work roundtrip each day,the following information is given: The point estimate for the true population mean is:

When finding sample size,cutting the margin of error in half requires that the sample size be four times larger.