Bus 308 Week 3

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Week 3 Assignment Kati Palmer BUS308: Statistics for Managers Dr. Ali A. Choudhry December 19, 2011 Week 3 Assignment 7.11 Suppose that we will randomly select a sample of 64 measurements from a population having a mean equal to 20 and a standard deviation equal to 4. a. Describe the shape of the sampling distribution of the sample mean bar x. Do we need to make any assumptions about the shape of the population? Why or why not? The shape of the sampling distribution of the sample mean bar x will be normal because there is a normal distribution. The Central Limit Theorem can be used since the sample is greater than 30. This eliminates the need to make assumptions. b. Find the mean and the standard deviation of the sampling distribution of the sample mean of bar x. Mean = 20 (given in the question) Standard deviation = 4/√64 Standard deviation = 4/ 8 Standard deviation = 0.5 c. Calculate the probability that we will obtain a sample mean greater than 21; that is, calculate P(x > 21). Hint: Find the z value corresponding to 21 by using μ and σ because we wish to calculate a probability about x. Then sketch the sampling distribution and the probability Z = (21-20)/ (4/√64) Z = 1/0.5 Z = 2 P (z>2) P = 1-0.9772 P = 0.0228 d. Calculate the probability that we will obtain a sample mean less than 19.385 ; that is calculate P(x.< 19.385). Z = (19.385 - 20)/ (4/√64) Z = -0.615 / 0.5 Z = -1.23 P = 0.1093 7.30 On February 8, 2002, the Gallup Organization released the results of a poll concerning American attitudes toward the 19th Winter Olympic Games in Salt Lake City, Utah. The poll results were based on telephone interviews with a randomly selected national sample of 1,011 adults, 18 years and older, conducted February 4-6, 2002. a. Suppose we wish to use the poll’s results to justify the

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