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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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You may need to use the appropriate appendix table or technology to answer this question. A magazine uses a survey of readers to obtain customer satisfaction ratings for the nation's largest retailers. Each survey respondent is asked to rate a specified retailer in terms of six factors: quality of products, selection, value, checkout efficiency, service, and store layout. An overall satisfaction score summarizes the rating for each respondent with 100 meaning the respondent is completely satisfied in terms of all six factors. Sample data representative of independent samples of Retailer A and Retailer B customers are shown below. Retailer A Retailer B n1 = 25 n = 30 x1 = 80 x2 = 71 (a) Formulate the null and alternative hypotheses to test whether there is a difference between the population mean customer satisfaction scores for the two retailers. (Let μ1 = population mean satisfaction score for Retailer A customers and μ2 = population mean satisfaction score for Retailer B customers.) H0: μ1 − μ2 ≥ 0 Ha: μ1 − μ2 < 0 H0: μ1 − μ2 < 0 Ha: μ1 − μ2 = 0 H0: μ1 − μ2 ≤ 0 Ha: μ1 − μ2 > 0 H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠ 0 H0: μ1 − μ2 ≠ 0 Ha: μ1 − μ2 = 0 (b) Assume that experience with the satisfaction rating scale of the magazine indicates that a population standard deviation of 12 is a reasonable assumption for both retailers. Conduct the hypothesis test. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = At a 0.05 level of significance what is your conclusion? Reject H0. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Do not Reject H0. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers. Reject H0. There is insufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Do not reject H0. There is insufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers. (c) Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. (Round your answers to two decimal places.) to Which retailer, if either, appears to have the greater customer satisfaction? The 95% confidence interval ---Select--- is completely above contains is completely below zero. This suggests that the Retailer A has a ---Select--- higher lower population mean customer satisfaction score than Retailer B.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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