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2. (5 points) A company's software has taken an average of 15 minutes to install. Changes have been made to the installation procedure, and a new sample of 41 installations has a mean of 14.5 minutes, with a standard deviation (of the sample itself) of 1.8 minutes. Using a level of significance a = 0.01, the company would like to claim that they have reduced the time of installation. (a) What is the population which is sampled? (b) Is this one or two tailed? One - tailed test (c) Clearly state both the null and alternative hypotheses. Ha: H. = 15: No reduction in the time of installation H. : to $ 15; reduction in the time of installation (d) Determine ferit and tampa sample has * = 14.5, 3 = 1.8 SX = 1. 8/ 141 = 0. 28 tart = 2. 473 + samp = ( 14.5- 15 ) /0.28 =-1.78 (e) What decision do you make about your hypotheses? Briefly, interpret this answer in terms of the actual situation - what is the company's reaction? We fail to reject Ho. (f) Construct a 98% confidence interval for the mean installation time