When estimating the mean, how large a sample must be used in order to assure a given level of confidence? Use the formula:

How do we determine the value of the population standard deviation,  ? Use the standard deviation, s, of a preliminary sample of size 30 or larger to estimate .

Determine the sample size necessary to determine (with 99% confidence) the mean time it takes to drive from Philadelphia to Boston. We wish to be within 15 minutes of the true time. Assume that a preliminary sample of 45 trips had a standard deviation of 0.8 hours.

... determine with 99% confidence... z 0.99 = 2.58

... We wish to be within 15 minutes of the true time.... E = 15 minutes = 0.25 hours

...a preliminary sample of 45 trips had a standard deviation of 0.8 hours. Since the preliminary sample is large enough, we can assume that the population standard deviation is approximately equal to 0.8 hours.

Minimum Sample Size =

Rounding Sample Size Any fractional value of n is always rounded to the next higher whole number.

Minimum Sample Size n  Round to the next higher whole number. To be 99% confident in our results, the minimum sample size = 69.

Formula for Minimum Sample Size for Estimating p for the Binomial Distribution If p is an estimate of the true population proportion,

Formula for Minimum Sample Size for Estimating p for the Binomial Distribution If we have no preliminary estimate for p, the probability is at least c that the point estimate r/n for p will be in error by less than the quantity E if n is at least:

Formula for Minimum Sample Size for Estimating p for the Binomial Distribution If we have no preliminary estimate for p, use the following formula to determine minimum sample size:

The manager of a furniture store wishes to estimate the proportion of orders delivered by the manufacturer in less than three weeks. She wishes to be 95% sure that her point estimate is in error either way by less than Assume no preliminary study is done to estimate p.

She wishes to be 95% sure... z 0.95 = 1.96

... that her point estimate is in error either way by less than E = 0.05

... no preliminary study is done to estimate p. The minimum required sample size (if no preliminary study is done to estimate p) is 385.

If a preliminary estimate indicated that p was approximately equal to 0.75: The minimum required sample size (if this preliminary study is done to estimate p) is 289.