Chapter 8
Interval Estimation
Case Problem 1: Young Professional Magazine
1. Descriptive Statistics for the quantitative variables follow:
Age
Investments
Transactions
Household Income
Mean
30.11
28538.29
5.97
74459.51
Standard Error
0.20
780.84
0.15
1719.55
Median
30
24800
6
66050
Mode
32
0
5
60300
Standard Deviator
4.02
15810.83
3.10
34818.21
Sample Variance
16.19
249982368.72
9.62
1212307794.38
Kurtosis
0.02
5.65
2.46
7.50
Skewness
-0.03
1.71
1.21
2.01
Range
23
133400
21
306300
Minimum
19
0
0
16200
Maximum
42
133400
21
322500
Sum
12346
11700700
2449
30528400
Count
410
410
410
410
Descriptive statistics for the qualitative variables follow:
Gender Male: 229 Proportion male: .5585
Plan R.E. purchase Yes: 181 Proportion yes: .4415
2. 95% Confidence Intervals
Age: 29.7215 to 30.5029
Household Income: $71,079 to $77,840
3. 95% Confidence Intervals
Broadband Access: .5775 to .6713
Have Children: .4859 to .5824
4. Young Professional should be a good advertising outlet for online brokers. We see that most of the
subscribers have financial investments exclusive of their home (the mean amount is $28,538) and
The mean number is approximately 6 per year and several subscribers make significantly more
5. The survey results allow us to estimate that the mean age of subscribers is 30.12 years and that
53.41% of subscribers have children. Given the age of subscribers, it is reasonable to assume that
their children are young. Thus, we conclude that subscribers to Young Professional would be a good
6. A variety of answers are possible here. But, from the survey results, it seems clear that articles about
investing would have appeal to many readers. Articles about real estate and architecture would
probably appeal to those subscribers planning to make a real estate purchase. Technology related
Case Problem 2: Gulf Real Estate Properties
The variables are as follows:
GV List The list price of a Gulf View condominium
GV Sale The sale price of the Gulf View condominium
GV Days The number of days to sell the Gulf View condominium
NGV List The list price of a No Gulf View condominium
1/2. A variety of descriptive statistics are shown below.
Descriptive Statistics: GV List, GV Sale, GV Days, NGV List, NGV Sale, NGV Days
Variable N Mean Median TrMean StDev SE Mean
GV List 40 474.0 437.0 462.0 197.3 31.2
GV Sale 40 454.2 417.5 441.2 192.5 30.4
GV Days 40 106.00 96.00 102.64 52.22 8.26
Variable Minimum Maximum Q1 Q3
GV List 169.9 975.0 332.7 551.9
GV Sale 165.0 975.0 314.3 530.6
GV Days 28.00 282.00 71.25 138.75
3. Gulf View condominiums are the more expensive as usually anticipated. A Gulf View
condominium lists for a mean price of $474,000 and a median price of $437,000. A No Gulf View
condominium lists for a mean price of $212,800 and a median price of $212,500. The Gulf View
condominiums are over twice as expensive as the No Gulf View condominiums.
The standard deviation of the list price for Gulf View condominiums is $197,300 and the standard
A Box Plot shows that the No Gulf View condominiums do not have any outliers. A similar box
plot shows the highest four Gulf View list prices are outliers: $885,000, $895,000 and two at
$975,000. These show 4/40 or 10% of the Gulf View condominiums have an unusually high list
price.
The mean number of days to sell a condominium is slightly better for Gulf View condominiums than
discount off the list price is roughly 4.0 to 4.5% for both Gulf View and No Gulf View condos.
4. Using the
unknown t procedure
Variable n Mean StDev SE Mean 95.0% CI
GV Sale 40 454.2 192.5 30.4 ( 392.7, 515.8)
GV Days 40 106.00 52.22 8.26 ( 89.30, 122.70)
95% Confidence Intervals:
Gulf View Mean Days to Sell 89 to 123
5. Using the
unknown t procedure
Variable n Mean StDev SE Mean 95.0% CI
NGV Sale 18 203.2 43.9 10.3 ( 181.4, 225.0)
NGV Days 18 135.0 76.3 18.0 ( 97.1, 172.9)
95% Confidence Intervals:
No Gulf View Mean Days to Sell 97 to 173
6. Gulf View condominiums
With n = 40, the margin of error is $59,600. To reduce the margin of error to $40,000 the
recommended sample size
No Gulf View condominiums
With n = 18, the margin of error is $21,800. To reduce the margin of error to $15,000 the
recommended sample size