1. An industrial engineer conjectures that a major difference between successful and unsuccessful companies is the percentage of their manufactured products returned because of defectives. In a study to evaluate this conjecture, the engineer surveyed the quality control departments of 50 successful companies (identified by the annual profit statement) and 50 unsuccessful companies. the companies in the study all produced products of a similar nature and cost. The percentages of the total output returned by customers in the previous year are provided in the attached file. a. Do the data provide sufficient evidence that successful businesses have a lower percentage of their products returned by customers? Use =0.1. b. What test did you use? What evidence do you have that the test's assumptions are valid? c. In order for the difference in percentage returns to have an economic impact, the difference must be at least 5%. Is there significant evidence that the percentage for successful businesses is at least 5% less than the percentage for unsuccessful businesses? d. Estimate the difference in the percentages of returns for successful and unsuccessful businesses using a 95% confidence interval. Does this result agree with the hypothesis test in part a? Why or why not? 'Unsuccessful Businesses' 'Successful Businesses' 11.35 10.24 8.34 5.43 6.56 5.09 8.93 3.62 8.26 4.06 9.19 6.16 7.69 6.32 6.85 8.2 7.32 2.23 7.07 7.7 10.3 5.06 13.58 0.43 8.06 10.51 13.7 1.08 12.23 8.32 8.59 10.64 10.49 7.3 7.71 1.94 8.67 9.16 11.93 6.33 4.98 6.77 11.07 0.47 11.04 9.82 10.08 6.07 4.76 3.83 6.82 10.13 6.92 0.82 11.69 6.69 8.53 7.51 13.81 4.96 6.03 4.59 9.77 9.34 9.4 0.91 9.14 4.46 11.41 9.05 11.15 1.38 9.36 2.39 10 6.17 9.02 2.13 6.44 6.41 9.38 8.81 8.39 11.06 5.45 0.17 6.7 2.41 9.5 0.27 8.32 1.97 7.98 4.19 9.67 7.47 5.66 7.24 8.99 8.48