Question

You are able to obtain, for a sample of 9822 individuals,

information about their alcohol consumption habits. This data is shown

in the excel spreadsheet named alcohol data.xlsx. The data contains the

following variables:

id: unique identier for each individual i

abuse before tax: takes value 1 if individual reports that she abused

of alcohol before the tax liquor was introduced in Calgary, 0 if she

reports that she did not abuse of alcohol before the tax liquor was

introduced in Calgary

abuse after tax: takes value 1 if individual reports that she abused of

alcohol after the tax liquor was introduced in Calgary, 0 if she reports

that she did not abuse of alcohol after the tax liquor was introduced in

Calgary

For person i in the sample, Yi denotes the change in alcohol abuse between

after and before the tax is introduced. The mean of Y in the population is

.

1. The null hypothesis is that there was no change in alcohol abuse after

the adoption of the tax on liquor. State this formally in terms of .

2. The alternative hypothesis is that there alcohol abuse decreased after

the adoption of the tax on liquor. State this formally in terms of .

Answer 1

This question is a classic example of Hypothesis testing, which is a statistical inference of asking a question, collecting the data related to it and then examining that data for further process. In most of the cases, Hypotheses is always about population statements (i.e. Y in this question).

The Hypotheses to be testes is called "Null Hypothesis" ; denoted as H₀. On the other hand, "alternative hypothesis" (H_a) covers outcomes not covered in Null hypothesis i.e. to prove alternative hypothesis, you must reject Null Hypothesis.

In the above example:

H₀: Yi = 0 ------------- ; Null Hypthesis of individuals (i) is zero because there was no change in alcohol abouse despite a tax introduction on alcohol.

H_a: Yi 0 --------------; Alternative Hypothesis of individuals (i) is alcohol abuse changes i.e. either increased or decreased after adoption of tax on liquor. This is one tailed testing as well. Alternative Hypothesis is further divided into one tailed and two tailed test. If we have to decide that population parameter (Y) is either greater or lesser than hypothesized value, then we use two tailed testing. Whereas, one tailed testing is done to determine if Y differs from hypothesized value in a specific direction (i.e. greater or lesser, not both can be tested).  

The above question in purview is about one tailed alternative Hypothesis testing as it stated if alcohol abuse "decreased" after the tax adoption in Calgary.

Null hypothesis: H₀: Yi = 0 ; no changes in alcohol abuse

vs.

Alternative Hypothesis: H_a: Yi < 0 ; alcohol abuse decreased after tax adoption on alcohol in Calgary