Topic4_StatisticalInferenceI_TestReview.pdf - ECO220Y5Y Quantitative Methods in Economics Topic Four \u2013 Statistical Inference I Test Review Questions

Topic4_StatisticalInferenceI_TestReview.pdf - ECO220Y5Y...

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ECO220Y5Y: Quantitative Methods in Economics Topic Four – Statistical Inference I Test Review Questions Tutorials – Fall/Winter 2017/18 Assume that the true proportion of UTM students who have taken at least one online distance course is .22. Suppose a sample of 500 students is selected. 1. Is the success/failure condition satisfied? Explain. 2. What would be the mean of this sampling distribution? What would be the standard deviation? 3. Sketch the histogram associated with the sampling distribution. ( hint: use the ‘68-95-99.7’ rule ) 4. What is the probability that the sample proportion will be less than .18? Tutorials – Fall/Winter 2017/18 It is generally believed that electrical problems affect about 14% of new cars. An automobile mechanic conducts diagnostic tests on 128 new cars on the lot. 1. Describe the sampling distribution of the sample proportion by naming the model and telling its mean and standard deviation. 2. What is the probability that in this group over 18% of the new cars will be found to have electrical problems? Tutorials – Fall/Winter 2017/18 Suppose that it is believed that 40% of adults have a company pension. If 100 adults are surveyed, 1. What is the probability of finding a sample with less than 30 adults having a company pension? 2. What is the probability of finding no more than 45 adults having a company pension? page 1 of 9
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ECO220Y January 15, 2020 Tutorials – Fall/Winter 2017/18 An investor is considering different money market funds. In the population there are an infinite number of alternative money market funds, but the average number of days to maturity for these funds can only take one of 4 alternative values and these occur with equal likelihood: 1. If you choose two of these funds at random, how many possible samples of two funds are there given that ordering is important? List the possible samples. 2. Find the probability function of the sampling distribution of the sample mean. 3. Verify that the mean of the sampling distribution is equal to the mean of the population and that the variance of the sampling distribution is the variance of the population divided by 2. 4. Write out the approximate sampling distribution of the sample mean if you take a sample of 100 of these funds at random. Write it out if you take a sample of 200. Explain how the distribution is changing as we increase the sample size. Tutorials – Fall/Winter 2017/18 The instructor in a particular statistics class claimed that the test this year was no harder than that in the previous year, when the average was 63.6% across all students. The students put together a random sample of 22 students and found the average sample test score was 59.8% with a standard deviation of 14%. 1. At the 5% significance level, test whether there is any substance in the instructors claim.
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