Question

Have you ever wondered what it means to click the “offset carbon emissions” button when you book a flight or train trip? It adds a small cost to your ticket, but how does this reduce emissions? The money is typically used to fund projects that reduce carbon emissions. One such project type is the introduction of more efficient cooking stoves into communities. Much of the world uses inefficient charcoal or wood stoves that result in excessive indoor air pollution, deforestation, and carbon emissions. Switching millions of families to more efficient stoves can result in a significant reduction in carbon emissions. [DATA ATTACHED BELOW]

In order for a project to claim carbon credits, they must provide accurate estimates of how much carbon that project is saving. An important parameter for cook-stove projects is the reduction in fuel that results from switching to the more efficient stove. Statisticians are needed to design the experiments; it is expensive to do these tests, so figuring out how big the sample size should be in order to get sufficiently accurate estimates, or to detect significant differences between the stove types, is important.

The EXCEL file, stove.xlsx, for this lab contains data from a pilot study using 19 randomly selected cooks. The numbers refer to the weight of firewood (in kg) to cook a regular meal. Each row in the spreadsheet corresponds to the same cook cooking the same meal. Use this data to answer the following questions. You may assume the conditions to carry out a hypothesis test are satisfied. You can assume (based on many similar studies) that the population standard deviation of reduction of firewood used is 0.7kg. Try to store as many decimal places as possible in intermediate steps.

1. For a project to qualify for carbon credits, the required precision for estimates of the amount of wood saved per new stove adopted is 90/10, i.e. the 90% confidence interval must have a margin of error no greater than 10% of the value of the estimate. Will the data from the pilot study enable the project to qualify for carbon credits?

2. What is the minimum sample size required to meet the 90/10 precision requirement?

3. Is there enough evidence to reject H0 at the α = 0.1 level of significance? What does this mean in context of this project?

4. What is the critical value of this hypothesis test at the α = 0.1 level of significance?

DATA:

Old Stove	Improved Stove	Reduction
3.9	1.8	2.1
3.8	2.65	1.15
3.65	1.5	2.15
3.2	2.2	1
2.6	1.25	1.35
2.4	1.65	0.75
2.3	1.4	0.9
2.25	1.7	0.55
2.2	2.15	0.05
2.1	1.8	0.3
2	1.4	0.6
2	1.05	0.95
1.9	0.8	1.1
1.9	1.75	0.15
1.8	0.55	1.25
1.55	0.9	0.65
1.4	1.3	0.1
1.4	1.1	0.3
1.15	0.75	0.4

Answer 1

We will set the null hypothesis

H₀   :

Vs

H₁ :

1. Under the null hypothesis the test statistics is

The results of the t.test are given below

Lower CI	Upper CI	T-Value	P-Value	DF
0.212	1.448	3.65	0.001	36

From the results of t.test it is evident that p.value = 0.001 which is less then 0.01 and we reject our null hypothesis and conclude that wood is saved per new stove.

2. Margin of Errors are given for the data

since