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Unformatted text preview: Economics 203 Midterm 1 Solutions — Fall 2009 — Form B 1. D. The sum of squares for error looks at the total variation within the multiple treatments by adding up the variances from the treatments. The SST looks at the variation between samples by squaring the differences of the grand mean with the treatment means. 2. C. A bellshaped 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. 3. E. Inference uses a sample to give us information about statistical population characteristics. 4. 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. 5. 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 α is the a priori probability that we will reject the null hypothesis when the null hypothesis is actually true. 6. E. This is a single population proportion question. The test statistic is found by . 4 . 5 √ . 5 * . 5 / 80 = 1 . 7889 7. D. You have a negative test statistic and would like to show that H 1 : p > . 50. This implies the pvalue is found by going from the test statistic to the extreme of the nearest rejection region (the far right of the normal distribution). And since the test statistic is negative this corresponds to choice (d). 8. D. The lower 90% confidence level for a single population proportion is found by . 4 1 . 645 * p . 4 * . 6 / 80 = 0 . 3099. 9. E. With no a priori information on the proportion of people who wash their hands, use the n = z 2 α/ 2 * . 5 2 w 2 formula. Then with a 90% interval, use 1.645 as the appropriate critical value and the sample size is then 1 . 645 2 * . 5 2 . 02 2 = 1691 . 26 and sample sizes are rounded up to 1692. 10. 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 onetailed test would result in a pvalue equal to 0.5....
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 Spring '10
 Petry
 Economics, Standard Deviation, Variance

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