Quarterbacks not only need to have a good passing percentage, but they need to be consistent. That is, the variability in the number of passes completed per game should be small. The table below gives the number of passes completed for Ben Roethlisberger and Aaron Rodgers, quarterbacks for the Pittsburgh Steelers and Green Bay Packers, respectively, during the 2010 NFL season. t Aaron Rodgers Ben Roethlisberger 19 21 7 16 20 19 15 25 19 22 34 27 19 17 21 12 22 17 23 27 26 30 22 18 21 18 15 (a) Does the data indicate that there is a difference in the variability in the number of passes completed for the two quarterbacks? Use a = 0.01. State the null and alternative hypotheses. O Ho: 012 = 022 versus Ha: 012 > 022 OH: 0 2 = 02 2 versus Ha: 01 2 02 State the test statistic. (Round your answer to two decimal places.) F = State the rejection region. (Round your answer to two decimal places.) F >5. Conclusion: O H is rejected. There is sufficient evidence to indicate that the supplier's shipments differ in variability. O Ho is not rejected. There is sufficient evidence to indicate that the supplier's shipments differ in variability. O Ho is not rejected. There is insufficient evidence to indicate that the supplier's shipments differ in variability. O Ho is rejected. There is insufficient evidence to indicate that the supplier's shipments differ in variability. (b) Find a 99% confidence interval for o, ". (Round your answers to three decimal places.) to Interpret your results. O 99% of all values will fall within the interval limits. O In repeated sampling, 1% of all intervals constructed in this manner will enclose o,. O There is a 1% chance that an individual sample variation will fall within the interval limits. O In repeated sampling, 99% of all intervals constructed in this manner will enclose o, O There is a 99% chance that an individual sample variation will fall within the interval.A pharmaceutical manufacturer purchases a particular material from two different suppliers. The mean level of impurities in the raw material is approximately the same for both suppliers, but the manufacturer is concerned about the variability of the impurities from shipment to shipment. If the level of impurities tends to vary excessively for one source of supply, it could affect the quality of the pharmaceutical product. To compare the variation in percentage impurities for the two suppliers, the manufacturer selects 10 shipments from each of the two suppliers and measures the percentage of impurities in the raw material for each shipment. The sample means and variances are shown in the table. Supplier A Supplier B X1 = 1.88 *2 = 1.84 s, 2 = 0.275 2 = 0.093 n1 = 10 n, = 10 (a) Do the data provide sufficient evidence to indicate a difference in the variability of the shipment impurity levels for the two suppliers? Test using a = 0.01. Based on the results of your test, what recommendation would you make to the pharmaceutical manufacturer? (Round your answers to two decimal places. ) 1-2. Null and alternative hypotheses: O Ho: 01 2 = 022 versus Ha: 012 + 02 OH: 0 2 = 02 2 versus H: 0 20,2 3. Test statistic: F = 4. Rejection region: F >