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Economics 154-257 Assignment 1 (due Jan.30, 2013) V.Zinde-Walsh 1. On a multiple-choice exam each of the 30 questions has 3 answers listed, one of...

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Economics 154-257 Assignment 1 (due Jan.30, 2013) V.Zinde-Walsh 1. On a multiple-choice exam each of the 30 questions has 3 answers listed, one of which is correct. Each correct answer is worth one mark, no marks deducted for incorrect answers. (a) A student got 16 out of 30. Test at 5% and 1% level of signi&cance whether the student was guessing on each question. Set the null and alternative hypotheses and test assuming that the sample is large enough for a normal approximation. (b) Find the prob-value (p-value). Test at 5% and 1% using the p-value. 2. A student is trying to decide whether on average rents for 2 1 2 apartments are higher in Verdun than NDG. In the classi&ed advertisments she &nds 12 listings in Verdun with an average rent of 450$/month with standard deviation $50, in NDG 10 listings with average rent of $400 and standard deviation of $90. Suppose that the rents may be treated as normally distributed with the same variance in the two areas, and the listings represent random independent samples. (a) Formulate the appropriate hypotheses and test at 10% level of signi&- cance. (b) If actually the rents are higher on average in NDG than in Verdun, discuss the correctness of the answer in (a). 3. The Ministry of Environment is allowing a plant to dump its e› uent into a river as long as it contains a maximum of 4 parts per million (ppm) of a toxic substance. In the course of one week the Ministry±s lab examines n = 64 samples of e› uent and &nds & X = 4 : 2 ppm of the toxic substance with a standard deviation s = 1 ppm. (a) Write down the hypotheses to test to determine whether the plant is in violation. (b) perform the test at 5% level of signi&cance. (c) construct the 90% CI for the mean. (d) Find the prob-value for the sample average. (e) Consider a second similar plant whose e› uent in n 2 = 100 samples gave & X 2 = 4 : 1 ppm and s 2 = : 5 ppm. Test the hypothesis with & = : 05 that there is no signi&cant di²erence in the amount of toxic substance in the e› uent between the two plants (assume equal variances in the two distributions). Describe what would be the e²ect on the test statistic if the variances are not assumed equal. 4. A health o¢ cial claims that the citizens of city A are &tter than those of city B. In city A 96 out of 200 selected at random passed a &tness test compared to only 84 out of 200 in city B. How valid is the claim? 5. To test the hypothesis that a coin is fair ( p = : 5) by tossing it a number of times we want to make sure that the probability of rejecting it when it is 1
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true is no greater than .05 and at the same time the probability of accepting it when actually p di/ers from .5 by .1 or more is also no greater than .05. Find the minimal sample size to satisfy these conditions. 2
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Ho: μ V ≤ μN
H1: μ V > μN
The test statistic is (450-400)/ SE
Where SE = (sp2/12+sp2/10) .5 = 31.74559 Sp2= [11*2500+9*8100]/20: spooled variance
The test statistic is equal to 1.57...

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