SAMPLE SIZE DETERMINATION FOR ESTIMATION OF MEAN MONTHLY RENTALS ts for lower income Housing in New York City a random sample of apartments is chosen and the rents are recorded. The housing authority wishestobe95%certainthattheerror In estimating the mean monthly rental is less than $50. How many apartments should Be In order to estimate the mean monthly rental of the 300,000 3 á room apartments in the sample? The standard deviation of rents is not known. APPROACHA: Additional Information It is discovered from the housing authority that it is extremely unlikely that the monthl rental of 3 4 room lower income apartments is outside the $750 to S1750 range.

Using this distributed and the "extremely unlikely" implies a probability of .05). ormation, determine the sample size. (HINT: Assume that rents are normally APPROACH B: Double Sampling A sample of 10 apartments is drawn and the following rents are obtained:

1. Estimate the mean rental and the standard deviation of apartment rentals from this 980, 1230, 1320, 1440, 1180, 1050, 1520, 1630, 880, 920 data and obtain a 95% confidence interval for the mean?

2. Is this sample mean an adequate estimate of the mean rental of the 3 ½ room lower 3. Using the data, 4. This method is called double sampling because we sampled the apartments income apartments in New York City?

 Discuss. estimate the sample size required by the housing authority. How many additional (if any) apartments must be sampled? to estimate the required sample size and a second time, if required, in order to once obtain an adequate disadvantages of this approach? Estimate of the mean rental. Discuss the advantages and twice?