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##### To whom it may concern: Please make sure to do a t-test in-(Answered)

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To whom it may concern:

Please make sure to do a t-test in question4 (c). Thanks

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

(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

9.1

6.8

7.4

8.3

12.7

8.7

7.3

7.6

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

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.

Paper#9256557 | Written in 27-Jul-2016

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