The following exercise requires the use of a computer and software. Use a 5% significance level for all tests. A person starting a new job always takes a certain amount of time to adjust fully. In repetitive-task situations, such as on an assembly line, significant productivity gains can occur within a few days. In an experiment to study this phenomenon, the average amount of time required for a new employee to install electronic components in a computer was measured for the first 10 days. These data are shown here. Day 1 2 3 4 5 6 7 8 9 10 Mean times 41 40 36 37 32 31 30 32 29 31 (minutes) Write the equation for each model. A first-order model and a second-order model were proposed. 1. Time = Bo + 81 Day + 2. Time = Bo + B1 Day + 82 Day? + e 3. Time = Po + 81 Day + 82 Day? + 83 Day' + 4. Time = Do + 1 Day + 82 Day? + By Day' + B Day* + Select the first-order model. Select the second-order model. ii (b) Analyze both models. Determine whether they are valid. Test the validity of the first-order model. State the hypotheses. 1. Ho : B1 = B2 = B3 = 0 H1 : At least one ; is not equal to zero. 2. Ho : B1 = B2 = Bg = B4 = 0 H1 : At least one ; is not equal to zero. 3. Ho : B1 = B2 = 0 H1 : At least one Bi is not equal to zero. 4. Ho : 81 = 0 H1 : 31 0 iv What is the test statistic? (Report the F-statistic. Round your answer to two decimal places.)H1 : At least one p; is not equal to zero. 4. Ho : 81 = 0 H1 : 31 0 iv What is the test statistic? (Report the F-statistic. Round your answer to two decimal places.) Use technology to find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. There is enough evidence to conclude that the first-model is valid. Test the validity of the second-order model. State the hypotheses. 1. Ho : B1 = B2 = By = 0 H1 : At least one ; is not equal to zero. 2. Ho : B1 = B2 = By = 84 = 0 H1 : At least one ; is not equal to zero. 3. Ho : B1 = B2 = 0 H1 : At least one ; is not equal to zero. 4. Ho : 81 =0 H1 : 81 0 i v X What is the test statistic? (Report the F-statistic. Round your answer to two decimal places.) Use technology to find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. There is enough evidence to conclude that the second-order model is valid. (c) Which model fits better? Explain. The second O-order model is slightly better because it has a |larger adjusted R? and a smaller standard error of estimate