Sherry is a production manager for a small manufacturing shop and is interested in developing a predictive model to estimate the time to produce an order of a given size-that is, the total time to produce a certain quantity of the product. Suppose she has collected data in the following table on the total time (in minutes) to produce 30 different orders of various quantities. Quantity Total Time (minutes) Quantity Total Time (minutes) 105 174 388 353 125 187 392 428 135 223 400 412 141 323 421 545 149 248 439 441 171 317 439 320 190 372 455 589 204 185 458 483 206 250 480 513 240 177 486 423 255 397 493 403 277 227 506 700 299 228 586 593 335 367 589 458 371 490 665 641 (a) Develop a scatter diagram with quantity as the independent variable. 800 700 700 600 600 500 500 400 Total Time (minutes) 400 300 300 200 200 100 100 o 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 800 O Quantity Total Time (minutes) 700 800 600 500 600 400 500 Quantity D 400 300 300 200 200 100 100 100 200 300 400 500 600 700 800 0 100 200 300 400 500 600 700 O Total Time (minutes) Quantity (b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? The scatter diagram indicates a nonlinear relationship between quantity and total time. The scatter diagram indicates a negative linear relationship between quantity and total time. The scatter diagram indicates no apparent relationship between quantity and total time. The scatter diagram indicates a positive linear relationship between quantity and total time. (c) Develop the estimated regression equation. (Let x = quantity, and let y = total time (in minutes). Round your numerical values to four decimal places.) y = Interpret the intercept and slope. The intercept is the production time per unit, and the slope is the estimate for the setup time. O The intercept is the production quantity per minute, and the slope is the estimate for the setup quantity. The intercept is the estimate for the setup time, and the slope is the production time per unit. The intercept is the estimate for the setup quantity, and the slope is the production quantity per minute. (d) Test for a significant relationship. Use 0.05. (Use the F test.) State the null and alternative hypotheses. O Ho: Fo = 0 Ha: Bo $ 0 OHO: Bo $ 0 Ha : Po = 0 OHo: B 1 $ 0 Ha : B1 = 0 OH: P1 20 Ha : B 1 0 OH: P1 = 0 Ha : B 1 0 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. O Reject Ho. There is a significant statistical relationship between quantity and total time. O Do not reject Ho. There is not a significant statistical relationship between quantity and total time. O Do not reject Ho. There is a significant statistical relationship between quantity and total time. O Reject Ho. There is not a significant statistical relationship between quantity and total time
