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# Appendix B, #1 - Suppose that a high school student is preparing to take the SAT exam. Explain why his or her eventual SAT score is properly viewed...

ANSWER only questions 1-6. Do NOT answer the rest. if you finish fast i will tip you good.
1. Appendix B, #1 – Suppose that a high school student is preparing to take the SAT exam. Explain why his or her eventual SAT score is properly viewed as a random variable. 2. Appendix B, #4 – For a randomly selected county in the United States, let X represent the proportion of adults over age 65 who are employed, or the elderly employment rate. Then, X is restricted to a value between zero and one. Suppose that the cumulative distribution function for X is given by F(x) = 3x^2 – 2x^3 for 0 <= x <= 1. Find the probability that the elderly employment rate is at least 0.6 (60%). 3. Suppose that the random variable (z) is distributed as a standard normal distribution. Using a standard normal table, calculate the following probabilities: a. Prob(Z ≤ -0.87) b. Prob(Z > 1.15) c. Prob(-1.1< z ≤ 1.67) 4. Suppose daily high temperatures (T) in June, July and August in a city are normally distributed with a mean of 87 and a standard deviation of 6.5 degrees. a) A family does not like to turn the air conditioning on until daily high temperatures are in excess of 92 degrees. On average, for what fraction of summer days will temperatures be in excess of 92 degrees? b) John is an avid golfer but he hates golfing in hot weather and will only golf when the daily high is 85 degrees or below. On average, what fraction of days will John be able to golf during the summer months? 5. Listed below are 10 values from two series. What is the correlation coefficient for x and y? X 1 3 5 7 9 11 13 15 17 19 Y 20 18 16 14 12 10 8 6 4 2 6. Below is a 2 x 2 table that lists the probabilities of the sex of a couple’s first child and whether a couple will have a second. For example, 15.7% of parents have a girl on the first child and never have a second.
Did the couple have a second child? No Yes Total Sex of first child Boy 0.149 0.339 0.488 Girl 0.157 0.355 0.512 Total 0.306 0.694 1.000 a) What is the Prob(Have a second child)? b) What is the Prob(Have a second child | 1st child is a boy)? c) What is the Prob(Have a second child | 1st child is a girl)? d) Using the results from a), b) and c) above, are the events ‘have a second child’ and ‘sex of the first child’ independent events. Why or why not? 7. Chapter 1, #C1 Use the data in WAGE1.dta for this exercise. (i) Find the average education level in the sample. What are the lowest and highest years of education? (ii) Find the average hourly wage in the sample. Does it seem high or low? (iii) The wage data are reported in 1976 dollars. Using the E conomic Report of the President (2011 or later), obtain and report the Consumer Price Index (CPI) for the years 1976 and 2010. (iv) Use the CPI values from part (iii) to find the average hourly wage in 2010 dollars. Now does the average hourly wage seem reasonable? (v) How many women are in the sample? How many men? 8. Chapter 1, #C2 Use the data in BWGHT.dta to answer this question. (i) How many women are in the sample, and how many report smoking during pregnancy? (ii) What is the average number of cigarettes smoked per day? Is the average a good measure of the “typical” woman in this case? Explain. (iii) Among women who smoked during pregnancy, what is the average number of cigarettes smoked per day? How does this compare with your answer from part (ii), and why? (iv) Find the average of fatheduc in the sample. Why are only 1,192 observations used to compute this average? (v) Report the average family income and its standard deviation in dollars.

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