(c) We want to test if there is a (positive) reduction in annual gas consumption provided by the extra insulation. Denote µx as the mean annual gas consumption for houses with standard insulation, and µy as the mean annual gas consumption for houses with extra insulation. (i) What are the null and alternative hypotheses?

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(c) We want to test if there is a (positive) reduction in annual gas consumption provided by
the extra insulation. Denote µx as the mean annual gas consumption for houses with
standard insulation, and uy as the mean annual gas consumption for houses with extra
insulation.
(i) What are the null and alternative hypotheses?
Transcribed Image Text:(c) We want to test if there is a (positive) reduction in annual gas consumption provided by the extra insulation. Denote µx as the mean annual gas consumption for houses with standard insulation, and uy as the mean annual gas consumption for houses with extra insulation. (i) What are the null and alternative hypotheses?
In a large scale study of energy conservation in single family homes, 20 homes were randomly
selected from homes built in a housing development in southern England. Ten of the houses,
randomly selected from the 20 houses selected for the study, were constructed with standard
levels of insulation (70 mm of roof insulation and 50 mm of insulation in the walls). The other
10 houses were constructed with extra insulation (120 mm of roof insulation and 100 mm of
insulation in the walls). Each house was heated with a gas furnace and energy consumption
was monitored for eight years. The data shown below give annual gas consumption in MWh
for each of the 20 houses.
Standard Insulation
Extra Insulation
13.8
15.1
17.8
13.9
18.0
15.9
17.3
17.2
16.9
15.2
19.9
13.8
13.6
11.3
17.6
13.2
15.9
18.8
12.3
14.0
Sample means
Sample Standard Deviation
16.31
14.84
2.38
2.12
Transcribed Image Text:In a large scale study of energy conservation in single family homes, 20 homes were randomly selected from homes built in a housing development in southern England. Ten of the houses, randomly selected from the 20 houses selected for the study, were constructed with standard levels of insulation (70 mm of roof insulation and 50 mm of insulation in the walls). The other 10 houses were constructed with extra insulation (120 mm of roof insulation and 100 mm of insulation in the walls). Each house was heated with a gas furnace and energy consumption was monitored for eight years. The data shown below give annual gas consumption in MWh for each of the 20 houses. Standard Insulation Extra Insulation 13.8 15.1 17.8 13.9 18.0 15.9 17.3 17.2 16.9 15.2 19.9 13.8 13.6 11.3 17.6 13.2 15.9 18.8 12.3 14.0 Sample means Sample Standard Deviation 16.31 14.84 2.38 2.12
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