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Econ 210 Winter 2008 Practice Questions Midterm IIa - Solutions_1

Econ 210 Winter 2008 Practice Questions Midterm IIa - Solutions_1

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Practice Questions IIa - Solutions 1. Assume you are sampling from a Normal Distribution with unknown mean and variance. a) You draw a sample of size 10 and calculate a sample mean of 33 and a sample variance of 225. Test the Null Hypothesis that the true mean of the distribution is equal to 22 and report the p-value. Also report if you can reject the null hypothesis at a 10%, 5%, 1% level. Calculate the t-statistic as 33 22 2.31 225 10 t - = = . This value would allow us to reject the null hypothesis at all levels a 10% (one-sided and 2-sided), 5% (one-sided and 2- sided). However, we don’t know the underlying distribution. Unless we know it is normal we cannot do the hypothesis test unless we take a bigger sample so that the CLT applies. b) Why is the above test not valid if the underlying distribution is not known? The CLT does not apply. 2. Assume you sample from Chi-square Distribution (mean K, variance 2K) a) What is the mean and variance of the sample mean?

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