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. You may read more about

such a project here.

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. Is this pilot study a matched pairs design? Briefly explain.

2. Are the variables “Old Stove” and “Improved Stove” independent? Briefly explain.

3. Create a new variable called “Reduction” which is defined to be “weight of firewood used for old stove

minus weight of firewood used for improved stove, in kg”. Are the values for “Reduction” independent?

Briefly explain.

4. What is the estimated mean reduction in firewood used (round to 4 decimal places)?

5. Find the 90% CI for the true mean reduction in firewood used. You may assume the population

standard deviation of reduction in firewood used is 0.7. What is the margin of error (round to 4

decimal places)?

6. 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?

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

8. We want to know if the weight of wood used with the improved stove is significantly less than the

weight of wood used with the old stove. State the null and alternative hypotheses for such a test.

9. Without performing any calculations for the hypothesis test, what will be a range of values of the

p-value based on the 90% confidence interval calculated in question 5 to test the hypothesis in question

8 at α = 0.10? Briefly explain. The options are

(a) p-value is less than 0.05

(b) p-value is less than 0.10

(c) p-value is greather than 0.05

(d) p-value is greater than 0.10

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

context of this project?

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

Old Stove |
Improved Stove |

3.9 |
1.8 |

3.8 |
2.65 |

3.65 |
1.5 |

3.2 |
2.2 |

2.6 |
1.25 |

2.4 |
1.65 |

2.3 |
1.4 |

2.25 |
1.7 |

2.2 |
2.15 |

2.1 |
1.8 |

2 |
1.4 |

2 |
1.05 |

1.9 |
0.8 |

1.9 |
1.75 |

1.8 |
0.55 |

1.55 |
0.9 |

1.4 |
1.3 |

1.4 |
1.1 |

1.15 |
0.75 |

Answer #1

1)

Yes, this is matched pairs study as similar groups are treated to two different conditions.

2)

Yes, the variables “Old Stove” and “Improved Stove” can be considered as independent as the treatments are different for both the groups.

3)

The variable Reduction is not independent as it depends on both the variables (“Old Stove” and “Improved Stove”).

4)

Mean Reduction = 0.8316

5)

Population Std Dev = 0.7

n = 19

At alpha = 0.1,

ZCritical = 1.64

Hence,

90% CI = 0.8316+/- 1.64 * 0.7/19^{1/2} =
{0.5682,1.0949}

PS: we are only allowed to answer 4 parts per question.

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