Estimation and Sample Size

The process of estimation is about making educated guesses about a population parameter based on the data gathered from a sample. The accuracy of such guesses highly depends on the sample size - the larger the sample, the more accurate the estimation. However, determining the perfect sample size is a matter of balancing between the necessary statistical precision and the resources available. It is also influenced by the confidence level and margin of error that are acceptable.

Finding Standard Error

A bottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company. The water bottling company's specifications state that the standard deviation of the amount of water is equal to 0.03 gallon. A random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.952 gallon. Complete parts (a) through (d). a. Construct a $99 \%$ confidence interval estimate for the population mean amount of water included in a 1-gallon bottle. $\leq \mu \leq$ (Round to five decimal places as needed.)