In order to estimate the mean monthly rental of the 300,000 3 ½ room apartments for lower income Housing in New York City a random sample of apartments is chosen and the rents are recorded. The housing authority wishes to be 95% certain that the error in estimating the mean monthly rental is less than $50. How many apartments should be in the sample? The standard deviation of rents is not known.
APPROACH A: Additional Information
It is discovered from the housing authority that it is extremely unlikely that the monthly rental of 3 ½ room lower income apartments is outside the $750 to $1750 range. Using this information, determine the sample size. (HINT: Assume that rents are normally distributed and the “extremely unlikely” implies a probability of .05).
APPROACH B: Double Sampling
A sample of 10 apartments is drawn and the following rents are obtained:
980, 1230, 1320, 1440, 1180, 1050, 1520, 1630, 880, 920.
1. Estimate the mean rental and the standard deviation of apartment rentals from this 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 income apartments in New York City? Discuss.
3. Using the data, estimate the sample size required by the housing authority. How many additional (if any) apartments must be sampled?
4. This method is called double sampling because we sampled the apartments twice, once to estimate the required sample size and a second time, if required, in order to obtain an adequate estimate of the mean rental. Discuss the advantages and disadvantages of this approach.
Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.
Read moreEach paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.
Read moreThanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.
Read moreYour email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.
Read moreBy sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.
Read more