3. Thirteen and ten items produced by two machines, old and new respectively, were selected at random and the times taken by the machines to produce the items are listed below: Machine Production...

Extracted text: 3. Thirteen and ten items produced by two machines, old and new respectively, were selected at random and the times taken by the machines to produce the items are listed below: Machine Production Times (in minutes) Туре Old 4 11 8 8 7 10 8 7 6 New 5 6 7 4 3 11 6 7 Assume that the production times are normally distributed, a. Are you 95% confident that the true variations in production times are not different regardless of the type of machines used? Justify your answer. [(0.187,2.493), Yes because ..] b. Use your answer in part (a) to construct a 95% confidence interval for the difference in the mean production times when the items are produced using old and new machines. Hence, verify if the new machine is significantly faster that the old machine in producing such items. [(-0.6039,2.8192), Yes because.]


Extracted text: The lifetime of 'Ener' and 'Gizer' light bulbs are assumed to be normally distributed. A random sample of 50'Enei light bulbs and 64 'Gizef light bulbs was tested. The following results (in hours) were obtained: Ener (X) Gizer (Y) Σ x = 128,000 y = 127,808 E(x- )? = 7987 20- ) = 9513 Find the 95% confidencein tenal for the difierence between the mean lifetime of the two brands of lightbutb. [(558.354,567.646)]