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Practice Problems

# Practice Problems - Econ 2500 Introductory Statistics York...

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1 Econ 2500 – Introductory Statistics York University Department of Economics Professor Xianghong Li Practice Problems Chapter 1 1. The states differ greatly in the kinds of severe weather that afflict them. Table ta01_005 shows the average property damage caused by tornadoes per year over the period from 1950 to 1999 in each of the 50 states and Puerto Rico. a. What are the top five states for tornado damage? The bottom five? b. Make a histogram of the data by hand, with classes "0 damage 10," "10 damage 20," and so on. Describe the shape, center, and spread of the distribution. Which states may be outliers? 2. ex01-035 presented data on the nightly study time claimed by first-year college men and women. The most common methods for formal comparison of two groups use x and s to summarize the data. We wonder if this is appropriate here. a. What kinds of distributions are best summarized by x and s ? b. Use R to draw separate histograms for men and women. c. Each set of study times appears to contain a high outlier. Are these points flagged as suspicious by the 1.5 IQR rule? How much does removing the outlier change x and s for each group? The presence of outliers makes us reluctant to use the mean and standard deviation for these data unless we remove the outliers on the grounds that these students were exaggerating. 3. Create a set of 5 positive numbers (repeats allowed) that have median 10 and mean 7. What thought process did you use to create your numbers? 4. Find the value z of a standard normal variable Z that satisfies each of the following conditions. (Using the normal table (Table A), report the value of z that comes closest to satisfying the condition.) In each case, sketch a standard normal curve with your value of z marked on the axis. a. 20% of the observations fall below z . b. 30% of the observations fall above z . 5. The Wechsler Adult Intelligence Scale (WAIS) is the most common “IQ test.” The scale of scores is set separately for each age group and is approximately normal with mean 100 and standard deviation 15. People with WAIS scores below 70 are considered mentally retarded when, for example, applying for Social Security disability benefits. What percent of adults are retarded by this criterion?

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2 6. The quartiles of any distribution are the values with the area to the left of the values and below the corresponding density curve to be 0.25 and 0.75. a. What are the quartiles of the standard normal distribution? b. Using the quartiles from (a), write an equation that gives the quartiles of an arbitrary normal distribution N (μ, σ ) in terms of μ, σ , and the two quartiles of the standard normal distribution. c. The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 266 days and standard deviation 16 days. Apply your results from (b): what are the quartiles of the distribution of lengths of human pregnancies?
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