An engineer has proposed the following model to describe the relationship between the number of acceptable items produced per day (output) and the number of work-hours expended per day (input) in a particular production process: 

y = β₀ + β₁x + β₂x² + ∈

where 

y = Number of acceptable items produced per day

x = Number of work-hours per day

A portion of the MINITAB computer printout that results from fitting this model to a sample of 25 weeks of production data is shown above (right column). Test the hypothesis that as amount of input increases, the amount of output also increases but at a decreasing rate. Do the data provide sufficient evidence to indicate that the rate of increase in output per unit increase of input decreases as the input increases? Test using α = .05.

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The regreasion equation is Y - -6.17 + 2.04 X1 -.0323 X2 SE Coef Predictor Constant Coef P -6.173 1.666 -3.71 0.002 0.000 -6. 60 0.0DO X1 2.036 . 185 11.02 X2 -.03231 .00489 S - 1.243 R-Sa - 95.5% R-Sa ladj) - 95.1% Analysis of Variance Source DF 33 P Regression 718.168 359.08 232. 41 0.000 Residual Error 22 33.992 1.545 Toral ?4 757 160