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 following table.
a. Do the data provide sufficient evidence that successful businesses have a lower percentage of their products returned by customers? Use α = .05.

b. Do the required conditions for applying your test in part (a) appear to be valid?
c. In order for the difference in percentage returns to have an economical impact, the difference must be at least 5%. Is there significant evidence that the percentage for successful businesses is at least 5% less that the percentage for unsuccessful businesses?
d. Estimate the difference in the percentages of returns for successful and unsuccessful businesses using a 95% confidence interval.

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Unsuccessful 11.35 9.19 1030 859 498 6.82 6.03 1115 9.38 8.32 Businesses 8.34 7.69 1358 1049 11.07 698 9.77 9.36 839 7.98 11.04 11.69 940 10.00 5.45 9.67 8.53 9.14 9.0 6.70 5.66 8.26 7.07 12.23 1193 4.76 138 14 644 950 8.99 5 8.67 10.08 2 6.56 6.85 8.06 7.71 893 7.32 13.70 Successful 10.24 6.16 5.06 10.64 6.77 10.13 459 138 881 1.97 Businsss 5.43 6.32 043 7.30 047 1082 9.34 2.39 11.06 4.19 1.94 9.82 6.69 0. 6.17 017 747 3.62 2.23 1.08 9.16 6.07 75 446 213 241 7.24 4.06 7.70 8.3 6.33 383 4.969.05 6.41 027 8.48 5.09 8.20 10.51