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Descriptive Numerical Analysis V3

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Project Description:

The present study investigates the distribution of sale prices for homes in a region in upstate New York. This project will also seek to compare the distributions of sale prices between homes with central air and homes without central air. Suppose you are being transferred to this area and are interested in getting a good description of selling prices for homes in this region. The variables collected in the data are: Price: Recorded in dollars; Lot size: measured in acres; Living Area: measured in square feet; Pct College: percent of students going to college; Central Air: No – 0, Yes – 1; Bedrooms: Number of bedrooms; Fireplace: Number of fireplaces; Bathrooms: Number of bathrooms. For the purpose of this project, you will only be using the variables Price and Central Air.

Instructions:

For the purpose of grading the project you are required to perform the following tasks:

Problem Housing Data

“The present study investigates the distribution of sale prices for homes in a region in upstate New York and to compare the distributions of sale prices between homes with central air and homes without central air. Suppose you are being transferred to this area and are interested in getting a good description of selling prices for homes there.

Use a cell reference or a single formula where appropriate in order to receive full credit. Do not copy and paste values or type values, as you will not receive full credit for your answers.

1-2) Obtain the descriptive statistics for sale prices for all homes in the dataset. Provide the values below:

Identify the mean sale price to the nearest cent in cell D7.
Identify the standard deviation of the sale prices to the nearest cent in D8.
Identify the minimum sale price to the nearest cent in cell D9.
Identify the first quartile sale price to the nearest cent in cell D10.
Identify the median sale price to the nearest cent in cell D11.
Identify the third quartile sale price to the nearest cent in cell D12.
Identify the maximum sale price to the nearest cent in cell D13.
Identify the sample size in cell D14.

To begin to construct the histogram of sale prices, we need to determine our bins. These are the upper limits to the size of the bars on the x-axis. We do this by calculating the range of the prices, and dividing by the number of bars we want in our histogram. Since we have a large sample size, let us choose to have about 25 bins.

3) Identify the range of sale prices in cell D18.
4) Calculate the size of the bins for 25 bins in cell D19.

5) Construct the histogram using the bins calculated. Follow the directions in step5 in the instructions document. Insert the histogram in cell C23.

Describe the distribution of housing prices of homes in upstate New York.

6) In cells F26-G26, choose how you would describe the shape of the distribution from the drop-down menu.
7) In cells F27-G27, choose which measure of ‘center’ is best to describe the distribution from the drop-down menu.
8) In cells F28-G28, choose how to compare the values of the mean and the median from the drop-down menu.
9) In cells F29-G29, choose which measure of ‘spread’ is best to describe the distribution from the drop-down menu.

Use the histogram (or the grouped frequency distribution) to answer the following.

10) In cell D34, calculate the percentage of homes rounded to one decimal place whose prices are expected to exceed \$300,000 using the value(s) found in step 5.

11) In cell D36, calculate the percentage of homes rounded to one decimal place that are priced between \$90,000 and \$300,001, exclusive, using the value(s) found in step 5.

12) In cell D38, calculate the percentage of homes rounded to one decimal place expected to be priced less than or equal to \$150,000 using the value(s) found in step 5.

13) Suppose you are looking at two houses in the same neighborhood that are about the same size except one of the homes has central air and the other one does not. Compare the distributions for homes with central air and homes without central air. Find the five-number-summary measures for homes with central air and for homes without central air.
Using the same bins you used in question 3), construct separate histograms for the sale prices for homes without central air and the sale prices for homes with central air. Title each histogram so that they are labeled appropriately by central air status. Insert the two histograms in cells B42-G42.

14-15) Obtain the descriptive statistics for sale prices for homes without central air and with central air in the dataset. Provide the values below. Round the monetary values to the nearest cent.
Without Central Air With Central Air
Minimum sale price, in cells D45 and E45
Q1, in cells D46 and E46
Median, in cells D47 and E47
Mean, in cells D48 and E48
Q3, in cells D49 and E49
Maximum, in cells D50 and E50
n, sample size, in cells D51 and E51

16) “Write a brief summary statement comparing the sale prices of homes with and without central air using the medians and the interquartile ranges as a general range of prices one would expect to pay for ‘typical’ homes in this region of upstate New York using the statements provided below.

“In cells D55 and D56, compare the estimated sale prices of homes with central air to homes without central air. Choose the correct answers from the drop-down menus.
Homes with central air generally sell for prices than homes without central air.
This is indicated by comparing the home prices between homes with and without central air.
Calculate the expected difference in median costs in cell E58. Keep the same number of decimal places as the values in step14 and step15.
Given this data, one would estimate that homes with central air can be expected to cost about more than homes without central air.
Identify the variability of prices using Q1 and Q3 for each data set in cells D60, F60, D61, and F61. Keep the same number of decimal places as the values in step14 and step15.
The variability of prices for the typical home without central air ranges from about to
as compared to to for homes with central air. Get Statistic Excel homework help today.

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