Homework 3

EAI Tech Fall 2009 Instructor : A. Dalmasso

Statistics for business

Homework # 3 Due date: Friday, November 27th

Exercise 1. Chapters 7 and 8 Determine the probabilities for the following normal distribution problems a) µ = 604, σ = 56.8, n = 10, P( X < 636) b) µ = 48, σ = 12, P(14 < X < 20) c) µ = 11, σ = 33.8, n = 50, P(9 ≤ X ≤ 15) d) µ = 37, σ = 17.35, n = 100, P( X ≥ 39) e) µ = 180, σ² = 129.96, P(X < 178) Exercise 2. Chapter 9 A process produces bags of refined sugar. The weights of the contents of these bags are normally distributed with standard deviation 1.2 ounces. The contents of a random sample of 25 bags had a mean weight of 19.8 ounces. Find the upper and lower confidence limits of a 99% confidence interval for the true mean weight for all bags of sugar produced by the process. Exercise 3. Chapter 10 A random sample of n = 25 is obtained from a population with variance σ²X = 225, and the sample mean is computed to be x = 70. Use this information and α = 10% to test the following hypotheses: H0 : µ = 80 versus the alternative hypothesis H1 : µ < 80. (Note : Don’t use the P-value method.)

Exercise 4. Chapter 10 Shell Oil claims that the average gasoline price of their brand is not equal to $1.25 per gallon. In order to test their claim, we randomly selected a sample of 49 of their gas stations and determined that the average price per gallon of the stations in the sample is $1.20. Furthermore, we assume that the standard deviation of the population is $0.14 from other studies. 1) Using an alpha of 0.10, test the company’s claim (Determine H0 and H1). State a conclusion. 2) Next, find the p-value. Do you find the same conclusion?