# Week 2, Homework 1 Essay

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Answers to Week Two Homework Assignment ( Assignment 1) Chapter 7 Exercise 13 You should choose a sample size of 1000 people. Although the law of averages tells you that the average of 1000 people is very likely to be close to 60 inches -- and thus under 65 inches tall -- here you are winning a prize for each person over 65 inches tall, not when the average of all the people is over 65 inches tall. Having a larger sample will give you more chances at getting the prize. The law of averages pertains to the variability of a sample average -- not variability in individual data values themselves. Here, we are concerned with individual data values. Chapter 7 Exercise 18 No, we can say we are quite confident that the average wage is between \$25 and \$35 per hour -- even though there might not be many employees who earned in that range. For example, if the city only has low-paying jobs and high paying jobs, the average could fall between \$25 and \$35 per hour with few workers, or even none, actually earning in that range. Chapter 7 Exercise 23 If the candidates are nearly tied, that means the standard error for the sample percentage would be the square root of (50×50/size of the sample). Since they want the margin of error to be equal to 1%, this means we would like the standard error to be equal to 0.5%. This means 0.5 = square root of (50×50/size of the sample). Solving for the size of the sample, sample size = (50/0.5) squared= 10,000 people. This is a very large sample. Chapter 8 Exercise 6 (a) \$300 to \$700 is plus or minus twice the SD for the population, and we can say that approximately 95 percent of all balances are in this range. (b) One correct answer to this part is as follows: We can say that we are 95 percent confident the average balance for all overdue bills is in the range from \$480 to \$520. Since the standard error SE for the sample mean should equal