1. The following observations are the estimated payback periods (in years) for installation of aluminium-framed double glazing in a random sample of ten homes in Christchurch. These periods reflect the costs of installation, and energy savings from the insulation.
|
12.5
|
20.3
|
22.3
|
19.7
|
19.5
|
|
24.5
|
26.9
|
13.4
|
18.4
|
18.3
|
(a) Draw a boxplot of these data. Do you think a normality assumption is reasonable?
(b) Calculate a 95% confidence interval for the mean payback period for this sort of retro-fitted double glazing.
(c) How large a sample would be needed to estimate the mean payback period to within one year?
2. "The Great Morality Debate" - an online survey of New Zealanders asked "is it wrong for men and women to have sex before marriage?" A staggering 35% of the 9000 responses were "yes" although there were strong regional differences (only of 23% of respondents from Wellington answered in the affirmative).
(a) Calculate a 95% confidence interval for the population proportion who believe it is wrong to have sex before marriage.
(b) Assume that the sample data exclude Wellingtonians, and that the population proportion for Wellingtonians is p=23%. Is the sample proportion significantly higher?
3. The following table contains weighted average cost of capital estimates(WACC, in %) for a random sample of New Zealand firms in two sectors: consumer and property.
|
Consumer
|
|
11.0
|
7.0
|
8.1
|
9.4
|
10.8
|
7.0
|
11.3
|
7.6
|
|
9.1
|
6.8
|
7.4
|
8.3
|
12.7
|
8.7
|
7.3
|
|
|
Property
|
|
6.8
|
8.7
|
7.0
|
7.1
|
6.9
|
7.2
|
7.2
|
6.8
|
Assuming the WACCs are normally distributed with different variances, conduct a test of equality of means.
4. The following retail website brand awareness figures are the percentage of survey respondents who recognized the website brand:
|
Website
|
%2009
|
%2010
|
|
Farmers.co.nz
|
0.7
|
3.1
|
|
Thewarehouse.co.nz
|
4.2
|
12.7
|
|
Woolworths.co.nz
|
2.0
|
5.1
|
|
Harveynorman.co.nz
|
1.0
|
0.0
|
|
Dse.co.nz
|
3.9
|
6.0
|
|
Noelleeming.co.nz
|
3.4
|
4.8
|
|
1-day.co.nz
|
5.2
|
7.3
|
|
Ezibuy.co.nz
|
4.2
|
5.4
|
|
Mightyape.co.nz
|
1.7
|
1.9
|
|
Foodtown.co.nz
|
2.2
|
2.4
|
|
Smilecity.co.nz
|
3.9
|
4.1
|
|
Apple.com
|
2.0
|
2.1
|
(Answer a and b, but do the t-test in c anyway, ensuring that you reflect on whether or not it was a good idea to do so.)
(a) Why is a paired comparison justified for these two samples?
(b) Why is a t-test inappropriate for these two samples?
(c) Test the hypothesis that website brand recognition is increasing for retail websites generally.