Question

3 Question 3 - Liquor Tax (25 Marks) by the governor to study whether a tax on liquor has decreased average liguor consumption in your state. You are able to obtain, for a sample of individuals selected at random, the difference in liquor consumption (in ounces) for the years before and after the tax. For person i, who is sampled randomly from the population, Y denotes the change in liquor consumption. That these as a rndoma sample from a Normal (ILO2) distribution You are hired 1. The null hypothesis is that there was no change in average liquor consumption, the alternative is that there was a change average liquor consumption. State the null and alternative hypothesis formally in terms of p. 2. Now suppose your sample size in n 900 and you obtain the estimates y -32.8 and s 4664. Calculate your test statistic for test Ho against Hi, what is the p-value? Do you reject Ho at the 10% level? 5% level? 1% level? (because of the large sample size, use the standard normal distribution tabulated at the end of the textbook). 3. Would you say the estimated fall in consumption is large in magnitude? Comment on the practical versus statistical significance of this estimate. 4. What has been implicitly assumed in your analysis about other determinants of liquor consumption over the two-year period in order to infer causality from the tax change to liquor consumption?

Answer 1

1)

H0:μ=0

H1:μ<0

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2)

Thep-value for the test isP(Z<-2.11) =0.0174

Hence, we will reject the null hypothesis at 5% level(0.05) and 10 % level (0.1)

and accept it at 1% level (0.01) because p-value is greater than 0.01 and less than 0.05 and 0.1

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We find a statistically significant decrease in consumption, at least at the 5% level and 10% level

Statistically, the fall in consumption is large but practically the fall in consumption is not affected by the tax change.

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4)

It can be said that for improved analysis of liquor consumption, the factors like changes in the habits of individuals over a period of time, reasons and consequence of consumption of liquor should be checked and taken into consideration.

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