PHYS5032 Techniques for Sustainability Analysis
Total points: 15
Homework Sheet 2: Hypothesis testing
1. Familiarise yourself with the Excel functions LINEST and TINV.
2. Download the data file HW02_data.xlsx here: http://bit.ly/2SC7Tye (also can be downloaded from canvas)
The local forest authority has asked you to undertake a study to examine whether the width of a tree trunk is linearly dependent on the age of the tree. You head out into the forest and measure 20 trees (see sheet “20 trees” in the Excel file).
3. (A) Plot the values in a scatterplot, calculate the regression coefficients ^α and ^β (using LINEST) and plot the regression curve into the scatterplot. (2 points)
4. (A) Perform a t-test for both coefficients for the following three type-I-error probabilities: 0.1, 0.05, 0.01. Does the linear model support a rejection of the null hypothesis if the significance level is 5%? (3 points)
The local forest authority wants to see statistical evidence that the null hypothesis is rejected at a type-I-error probability of 1%. In order to give you more underlying data, the forest authority provides 20 additional measurements. These new measurements together with the measurements that you have already investigated are available in the sheet “40 trees” in the Excel file. From now on, work with the 40 trees dataset.
5. (A) Plot the values in ascatterplot, calculate the regression coefficients, and plot the regression curve into the scatterplot. (2 points)
6. (A) Perform a t-test for the following three significance levels: 0.1, 0.05, 0.01. Does the new dataset satisfy the requirement regarding the type-I-probability as demanded by the forest authority? (2 points)
7. In your own words (A): Consider you calculate the tinv value for a type-I-error probability of 10% and 5%. Which tinv value is higher and why? (3 points)
8. In your own words (A): Discuss potential reasons why the 20-tree-dataset does not support a rejection
of the null hypothesis at lower type-I-error probabilities, but the 40-tree-dataset does. (3 points)
Remember, the main aim is to show that you understand the concepts of hypothesis testing. So, make sure you write you results down as if you were using them as examples to explain hypothesis testing to somebody who is just learning about it.