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Name: Statistics Davidson College Economics 105, Aug-Dec 2004 Mark C. Foley
Review # 2
Due in Ch. 3140 by 5 p.m. Friday. Directions : This review is closed-book, closed-notes (except for your formula sheet) to be taken in one sitting of unlimited time. You may use a calculator. You may not use Excel. Perform your calculations to 3 decimal places, where necessary. There are 100 points on the exam. Each problem is worth 20 points. You must show all your work to receive full credit. Any assumptions you make and intermediate steps should be clearly indicated. Do not simply write down a final answer to the problems without an explanation. Please turn in your formula sheet with your exam. Carpe diem. Honor Pledge Start time End time
Assume that X, the price of one share of stock X, and Y, the price of one share of stock Y, are jointly distributed random variables with the following joint probability function: X 0 1 2 Y 0 0 .1. 1 .2 .2. (a) Calculate and interpret the correlation between X and Y. (b) What is the variance of a portfolio consisting of 3 shares of stock X and 2 shares of stock Y? That is, find the variance of 3X + 2Y.
(a) As shift manager at a local restaurant, you are responsible for quality control. You don’t want to weigh all the frozen hamburger patties that get delivered by your supplier to make sure they weigh 4 ounces on average, so you have one of your workers do it. Assume that the standard deviation of the weight of all hamburger patties is known to be 0.1 ounces. You tell your employee to select 20 patties at random from the shipment, weight them, and reject the shipment if the average weight is less than 3.95 ounces. What is the significance level associated with your decision rule? State any assumptions. (b) Using a properly labeled diagram (and without doing more calculations), explain how and why the critical value in part (a) would change if you tell your worker to select more than 20 patties.
(a) A student, who lives off-campus, records the time in minutes it takes to commute for 7 seven days: 21 15 13 16 10 13 18 Assuming the population is normally distributed, find and interpret a 95% confidence interval for the population mean. (b) Using a properly labeled diagram (and without doing more calculations), explain how and why the confidence interval in part (a) would change if the significance level changed to 1%.
(a) State, precisely, the Central Limit Theorem. (b) Using a graph for the population distribution and a different graph for the sampling distribution, illustrate and explain the central limit theorem. Label all axes and curves.
