Due to a crisis in subprime lending, obtaining a mortgage has become difficult e
ID: 3244154 • Letter: D
Question
Due to a crisis in subprime lending, obtaining a mortgage has become difficult even for people with solid credit. In a report by the Associated Press (August 25, 2007), sales of existing homes fell for a 5th consecutive month, while home prices dropped for a record 12th month in July 2007. Elvis Presley, a research analyst for Expert Quants, wishes to study how the mortgage crunch has impacted the once-booming market of Florida. He collects data on the sale prices (in $1,000s) of 30 single-family homes in Fort Myers, Florida, in January 2007 and collects another sample in July 2007. For a valid comparison, he samples only three-bedroom homes, each with 1,500 square feet or less of space on a lot size of 10,000 square feet or less. Sales data for this case study can be found in the accompanying Excel. Use the sample data Excel file and compute following statistics: 1. The mean, the median, and the mode in each of the two sample periods (January and July). 2. The standard deviation in each of the two sample periods. Is there anything that catches your attention when you compare the two standard deviations? 3. If an average house, meeting the same criteria as above, sells nationally for $250,000 in January and $210,000 in July how does Ft Myers compare? (Hint: Compute the z-score for January and July assuming your calculated means are x for each of the periods). 4. Write an informative report and discuss your all findings from number 1 – 3. Submit your calculations along with your report.
Number January (in $1,000s) July (in $1,000s) 1 100 136 2 190 235 3 125 97 4 610 179 5 260 156 6 167 200 7 255 219 8 205 400 9 256 86 10 330 215 11 460 125 12 242 133 13 220 199 14 140 210 15 158 255 16 130 148 17 144 210 18 176 126 19 220 120 20 231 285 21 160 202 22 315 218 23 143 90 24 340 144 25 200 180 26 150 175 27 212 200 28 189 295 29 450 180 30 275 515Explanation / Answer
Answer:
Due to a crisis in subprime lending, obtaining a mortgage has become difficult even for people with solid credit. In a report by the Associated Press (August 25, 2007), sales of existing homes fell for a 5th consecutive month, while home prices dropped for a record 12th month in July 2007. Elvis Presley, a research analyst for Expert Quants, wishes to study how the mortgage crunch has impacted the once-booming market of Florida. He collects data on the sale prices (in $1,000s) of 30 single-family homes in Fort Myers, Florida, in January 2007 and collects another sample in July 2007. For a valid comparison, he samples only three-bedroom homes, each with 1,500 square feet or less of space on a lot size of 10,000 square feet or less. Sales data for this case study can be found in the accompanying Excel. Use the sample data Excel file and compute following statistics:
1. The mean, the median, and the mode in each of the two sample periods (January and July).
Descriptive statistics
January (in $1,000s)
July (in $1,000s)
n
30
30
mean
235.10
197.77
median
208.50
189.50
mode
220.00
200.00
2. The standard deviation in each of the two sample periods. Is there anything that catches your attention when you compare the two standard deviations?
Descriptive statistics
January (in $1,000s)
July (in $1,000s)
n
30
30
sample standard deviation
112.69
89.47
standard deviation of January is larger than July.
3. If an average house, meeting the same criteria as above, sells nationally for $250,000 in January and $210,000 in July how does Ft Myers compare? (Hint: Compute the z-score for January and July assuming your calculated means are x for each of the periods).
Z score for January, z =(250-235.10)/112.69 =0.132
Z score for July, z =(210-197.77)/89.47 = 0.136
Since z scores are almost same, sale in January and July are same.
4. Write an informative report and discuss your all findings from number 1 – 3. Submit your calculations along with your report.
There are 30 sales prices for January and July. The average sales price for January is $235.10(in 1000) with standard deviation is 112.69. The average sales price for July is $197.77(in 1000) with standard deviation is 89.47. The minimum sale price in (in 1000) January is 100 and maximum is 610. The minimum sale price in (in 1000) July is 86 and maximum is 515. Compared to national averages both month sales are similar.
Descriptive statistics
January (in $1,000s)
July (in $1,000s)
count
30
30
mean
235.10
197.77
sample standard deviation
112.69
89.47
sample variance
12,700.16
8,004.25
minimum
100
86
maximum
610
515
range
510
429
1st quartile
158.50
138.00
median
208.50
189.50
3rd quartile
259.00
217.25
interquartile range
100.50
79.25
mode
220.00
200.00
Descriptive statistics
January (in $1,000s)
July (in $1,000s)
n
30
30
mean
235.10
197.77
median
208.50
189.50
mode
220.00
200.00
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