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3. One of the major measures of the quality of service provided by any organization is the speed with which it responds to customer complaints. A large family-held department store selling furniture and flooring, including carpeting, had undergone a major expansion in the past several years. In particular, the flooring department had expanded from 2 installation crews to an installation supervisor, a measurer, and 15 installation crews. A sample of 50 complaints concerning carpeting installation was selected during a recent year. The following data represent the number of days between the receipt of the complaint and the resolution of the complaint.,54 5 35 137 31 27 152 2 123 81 74 27,11 19 126 110 110 29 61 35 94 31 26 5,12 4 165 32 29 28 29 26 25 1 14 13,13 10 5 27 4 52 30 22 36 26 20 23,33 68,a. The installation supervisor claims that the mean number of days between receipt and of a complaint and the resolution of the complaint is 20 days. At the 0.05 level of significance, is there any evidence that the claim is not true (i.e., that the mean number of days is different then 20)?,b. What assumption about the population distribution is needed in order to conduct the t test in (a),

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