Results of multiple regression for Defect Summary measures Multiple R 0.9383 R-Square 0.8803 Adj R-Square 0.8612 StErr of Est 7.2326 ANOVA Table Source df SS MS F p-value Explained 4 9621.5292 2405.3823 45.9828 0.0000 Unexplained 25 1307.7628 52.3105 Regression coefficients Coefficient Std Err t-value p-value Constant 1.0312 73.8985 0.0140 0.9890 Temperature 17.4189 9.5635 1.8214 0.0805 Density -1.5741 1.7446 -0.9022 0.3755 Rate 0.1184 0.1330 0.8904 0.3817 Morning -0.9186 3.0655 -0.2997 0.7669 Use the output above to answer parts (h) through (l). h) Returning to the p-value for the indicator variable Morning, what conclusion can you draw? i) Using non-technical language, state and interpret the standard error of the estimate. j) Is Rate significant? What does Rate’s significance or lack thereof imply about controlling the production quality? In particular, should you be slowing down the production rate as Ole has stated? k) What action would you take to lower the number of defects? Be specific. l) What is the expected number of defects when the standard deviation in temperature is 1, the density is 25, the rate is 200, and produced by the morning shift? _____________________________________________________________________________________________________________________ 2. You have tested a new system that supposedly reduces variable costs of production. Because the new system involves additional expenditures, you calculated that you would be willing to use the new system only if variable cost would be less than $6.27 per unit produced. Based on careful data collection and analysis of the new system, you found that the average variable cost under the new system is $6.05. a) State the null and alternative hypothesis. Make sure you clearly and completely define all conclusions you can draw from the output? Null Hypothesis: Alternative Hypothesis: b) Based on the information above, would you go with the new system? Why or why not? c) Would your answer change if average variable cost under the new system is $1.05? d) Assuming you reject the null hypothesis you stated above, explain the business ramifications of making a Type 1 error. 4. You have been promoted to manage a new line of low-calorie frozen dinners produced by your firm. These dinners have been selling very well, and the competition is starting to heat up. Your task is to continue gaining market share and hold off competing brands. You have not been on the job long when you find out the even though these dinners are advertised as being low calorie, nobody has been measuring the calorie content as part of the quality assurance. You and your competitors advertise that your dinners have 200 calories. You have asked the quality assurance people to measure the calorie content of your and your competitors’ dinners. Below is the one of the 4 daily reports you have received over the last week. This report is similar to the others you have read. Two-sample analysis for Calories__Us minus Calories__Them Summary stats for two samples Calories__Us Calories__Them Sample sizes 12 12 Sample means 208 197 Sample standard deviations 11 14 Test of difference<=0 versus one-tailed alternative Hypothesized mean difference 0.000 Sample mean difference 11.0 Pooled standard deviation 12.6 Std error of difference 5.1 Degrees of freedom 22 t-test statistic 2.130 p-value 0.022 a) Should you be concerned with the results, or is all well? b) Could these results impact your task of increasing market share? Explain.