Handout on Finding the Sample Size Needed for a Confidence Interval for a Single Population Mean Table of z-values for commonly used confidence levels Suppose you want to construct a 95% confidence interval for the mean age that people have their wisdom teeth removed.  If you know that the standard deviation is 1.8 and you want a margin of error of no more than plus or minus 0.2 years, at least how many people must you survey? Solution Past research has shown that the standard deviation for the number of pencils and pens that college students use in a quarter is 4.2.  If you want to construct a 90% confidence interval for the mean number of pencils and pens that college students use in a quarter and if you want to have a margin of error of no more than plus or minus 0.3 at least how many students must you survey? It is known that that the standard deviation for the number of hours of sleep that students get each night is 2.1.  If you want to construct a 95% confidence interval for the mean hours of sleep that students get each night and if you want to have a margin of error of no more than plus or minus 0.1 at least how many students must you survey? You have just conducted a preliminary survey of 22 students asking them how many times a week they eat in fast food restaurants.  The standard deviation for this survey was 2.8.  If you want to construct a 95% confidence interval for the mean number of times per week students eat in fast food restaurant and have a margin of error no more than plus or minus 0.05, at least how many additional students must you survey? Solution You have just conducted a preliminary study of 16 gas stations to determine how many cents per gallon their profit is.  The standard deviation for this study was 8.3.  If you want to construct a 95% confidence interval for the mean cents per gallon that all gas stations profit and have a margin of error no more than plus or minus 0.5 cents, at least how many more gas stations must you include in your study? You have just conducted a preliminary study of 12 people with depression and determined that the standard deviation for the number of ounces of alcohol that they consume each week is 18 ounces.  If you want to construct a 99% confidence interval for the mean number of ounces that people with depression consume per week and have a margin of error no more than plus or minus 2 ounces, at least how many people with depression must you include in your study? For questions 7 through 10, answer true or false and give your reasoning. Increasing the sample size while holding the level of confidence fixed will decrease the margin of error for a confidence interval. Solution Decreasing the level of confidence while holding the sample size fixed will increase the margin of error. Tripling the sample size while holding the level of confidence fixed will decrease the margin of error by a factor of 3. If the margin of error is to be decreased by a factor of 2 while holding the level of confidence fixed, then the sample size must be increased by a factor of 4.