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Unformatted text preview: Economics 203 Midterm 1 Solutions Fall 2009 Form A 1. C. A bell-shaped distribution with extremely high values added in to the right end of the distribution skews positively. The mean is more affected by extreme values than the median and so the median has to be less than the mean. 2. E. The steps in the hypothesis testing process involve setting the hypotheses and then sig- nificance level. You would then gather data, calculate a point estimate, then test statistic, and finally make a conclusion to your hypothesis by comparing the test statistic to the appropriate critical value based on the significance level and hypothesis. 3. C. These are dependent samples as the time is recorded for exactly the same puzzle between Joe and Josh. This reduces the noise that would be introduced into the analysis if random puzzles were given to Joe and another set of random puzzles were given to Josh. 4. D. This is a difference in proportions set up since you either own a car or not. The statement about more likely than the other says that the hypothesized mean difference is equal to zero. 5. C. This is a 2 for single population variance since you have a population standard deviation you are interested in exploring with a sample. 6. E. Inference uses a sample to give us information about statistical population characteristics. 7. E. All of the statements (A)-(D) are not true. The test statistic needs to be more extreme than the critical value. If we do not reject or reject, we may be right or wrong. And is the a priori probability that we will reject the null hypothesis when the null hypothesis is actually true. 8. A. This is a difference in proportions question. The relevant point estimate is 80/120 - 64/96 = 0. Thus the test statistic would equal zero. This is a one tailed test which goes to the left end of the z distribution. Since the z distribution is symmetric, a test statistic of 0 with a one-tailed test would result in a p-value equal to 0.5. 9. A. The empirical rule tells us that within 2 standard deviations, we expect to see 95% of the data. This implies that 5% will be outside of 2 standard deviations from the mean. Now the empirical rule further tells us that the distribution is symmetric so we assume 2.5% is in each tail. Thus there are 2 standard deviations between 65 and 95 and we want the area beyond 95 days, this corresponds to 2.5% then. 1 10. D. To go between confidence intervals and hypothesis test conclusions, you need to make sure that the from the confidence interval matches the two-tailed hypothesis . In this case, for a 15% level of significance you need a corresponding 85% confidence interval. A 85% confidence interval will be smaller than a 90% interval. Thus, .21 would absolutely still85% confidence interval will be smaller than a 90% interval....
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This note was uploaded on 07/19/2010 for the course ECON ECON203 taught by Professor Petry during the Spring '10 term at University of Illinois at Urbana–Champaign.
- Spring '10