STAT6003 Statistics for Financial Decisions: House Price Index

This assignment provides a statistical analysis of house price indexes in Brisbane, Sydney, and Melbourne. It examines the distribution of price indexes in each city, noting the skewness in Brisbane and Sydney, and the near-normal distribution in Melbourne. The mean, standard deviation, and 95% confidence intervals are calculated for each city's house price index. Hypothesis tests are conducted to determine if the mean house price index of each city is different from 100, and whether the population mean house price indexes differ between pairs of cities. The conclusion summarizes the key findings, including the relationship between mean and median price indexes, the confidence intervals, and the comparisons of mean price indexes across the three cities. Desklib offers a range of study tools and solved assignments to support students.

Statistics for Financial
Decisions

50-65 65-80 80-95 95-110 110-125
0
1
2
3
4
5
6
7
8
Distribution of Price Index at Brisbane
bin
Frequency
The price index of houses at Brisbane is left skewed, i.e., the median
price index is higher than the mean price index at Brisbane (Black
2016).

The price index of houses at Sydney is right skewed, i.e., the median
price index is lower than the mean price index at Brisbane (Black 2016).
76 -96 96-116 116-136 136-156 156-176
0
1
2
3
4
5
6
7
8
Distribution of Price Index at Sydney
bin
Frequency

The price index of houses at Melbourne seems to be normally
distributed
50-70 70-90 90-110 110-130 130-150
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Distribution of Price Index at Melbourne
bin
Frequency

House Price Index at Brisbane
Statistics Value
Mean 94.97
Standard Deviation 20.01
Lower Limit 84.84
Upper Limit 105.10
The mean house price index at Brisbane is 94.97. The standard
deviation of price index is 20.01. Thus the 95% confidence interval for
price index at Brisbane is 84.84, 105.10.

House Price Index at Sydney
Statistics Value
Mean 105.83
Standard Deviation 29.66
Lower Limit 90.82
Upper Limit 120.84
The mean house price index at Sydney is 105.83. The standard
deviation of price index is 29.66. Thus the 95% confidence interval for
price index at Sydney is 90.82, 120.84.

House Price Index at Melbourne
Statistics Value
Mean 92.75
Standard Deviation 27.96
Lower Limit 78.60
Upper Limit 106.90
The mean house price index at Melbourne is 92.75. The standard
deviation of price index is 27.96. Thus the 95% confidence interval for
price index at Melbourne is 78.60, 106.90.

Test whether the mean house price index of Brisbane, Sydney, Melbourne is
different than 100
Null Hypothesis: The mean house price index of Location is equal to 100
Alternate Hypothesis: The mean house price index of Location is not equal to 100

Statistics Value
Count 15
Mean 94.967
Std dev 20.012
Std Err 5.167
hyp mean 100
a 0.05
tails 2
df 14
t stat -0.974
p value 0.347
t crit 2.145
The t-stat value is -0.974.
Since, the t-stat value is less extreme
than t-crit value hence the Null
Hypothesis is not rejected. Thus, the
mean house price index at Brisbane is
equal to 100
Brisbane House Price
Index

Statistics Value
Count 15
Mean 105.827
Std dev 29.661
Std Err 7.658
hyp mean 100
a 0.05
tails 2
df 14
t stat 0.761
p value 0.459
t crit 2.145
The t-stat value is 0.761.
Since, the t-stat value is less extreme
than t-crit value hence the Null
Hypothesis is not rejected. Thus, the
mean house price index at Sydney is
equal to 100
Sydney House Price Index

Statistics Value
Count 15
Mean 92.753
Std dev 27.957
Std Err 7.219
hyp mean 100
a 0.05
tails 2
df 14
t stat -1.004
p value 0.332
t crit 2.145
The t-stat value is -1.004.
Since, the t-stat value is less extreme
than t-crit value hence the Null
Hypothesis is not rejected. Thus, the
mean house price index at Melbourne
is equal to 100
Melbourne House Price
Index

Test whether the population mean house Price Index for these cities is different for
each pair of cities.
Null Hypothesis: The mean price index of City 1 is equal to the mean price index of
City 2
Alternate Hypothesis: The mean price index of City 1 is different than the mean price
index of City 2
Decision Rule: At 0.05 level of significance and 14 degrees of freedom t-crit values
for two-tailed t-test are -2.145, 2.145. Thus, if the calculated t-stat is more extreme
than t-crit values then we reject Null Hypothesis else accept Alternate Hypothesis