Suppose you take a random sample of size n and look

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9) Suppose you take a random sample of size n and look at the average x . As n increases, which of the following statements is true? a) The mean of x ( X μ ) increases b) The mean of x ( X μ ) decreases c) The mean of x ( X μ ) stays the same d) We can’t tell what will happen to the mean of x ( X μ ) 10)Extrapolation means predicting Y between two values of X where data was collected. a) True b) False 2
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11) A random variable X has mean µ x and standard deviation σ x . Suppose n independent observations of X are taken and the average x of these n observations is computed. If n is very large, the law of large numbers implies: 12) A researcher is interested in the size of the current balance of credit card holders. To estimate this, he obtains the size of the current balance of a random sample of 37 credit card holders. A 95% confidence interval for the mean current balance of credit card holders is found to be $662.72 ± $44.70. Which of the following would produce a confidence interval with a smaller margin of error than this 95% confidence interval? 13)Suppose that 80% of all university basketball players graduate. You take a random sample of 100 university basketball players and find that 75% of them graduated. Which of these numbers represents the statistic in this problem? 14) A 98% confidence interval for the mean µ x of a population is calculated from a random sample and is found to be 25 ± 5. Which of the following could be the 93% confidence interval based on the same random sample? a) 25 ± 2 b) 25 ± 5 c) 25 ± 7 d) 25 ± 0 e) It could be any of the above 15) A survey is conducted to study the backgrounds of professional golfers. A random sample of 300 professional golfers was surveyed. The question they were asked was: “Did your parents play golf?” 10% of the golfers said yes. Let X be the number of professional golfers in the sample that said yes. X has a binomial distribution and can also be approximated by a normal distribution . Is the underlined statement true or false? 3
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