statistics help
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 9 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 = 1.86 *, = 1.84 ,2 = 0.275 S 2- 2 = 0.094 n1 = 9 n, = 9 (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: 012 = 02 versus Ha : 012 62 O Ho: 1 2 = 02 2 versus Ha : 01- 5, 2 # 02 O Ho: 01- 2 02 3. Test statistic: F = 4. Rejection region: F > 5. Conclusion: Ho is rejected. There is insufficient evidence to indicate that the supplier's shipments differ in variability. O H is not rejected. There is insufficient evidence to indicate that the supplier's shipments differ in variability. O Ho 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. (b) Find a 99% confidence interval for 2. (Round your answers to three decimal places.) to |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 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. OH:01 2 = 02 versus Ha: 012 # 02 OH: 0 2 = 0, 2 versus H : 0 1 2 02 OH: 0 12 = 02 2 versus Ha: 012 = 02 OH: 0 1 2 = 02 2 versus Ha : 012 > 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 > State the conclusion. O Ho is not rejected. There is insufficient evidence to indicate a difference in the variability. O Ho is rejected. There is insufficient evidence to indicate a difference in the variability. O Ho is not rejected. There is sufficient evidence to indicate a difference in the variability. O Ho is rejected. There is sufficient evidence to indicate a difference in the variability.The SAT subject tests in chemistry and physics for two groups of 13 students each electing to take these tests are given below. Chemistry Physics X = 647 X = 659 S = 115 s = 101 n = 13 n = 13 To use the two-sample t-test with a pooled estimate of of, you must assume that the two population variances are equal. Test this assumption using the F-test for equality of variances. (Use a = 0.05.) State the null and alternative hypotheses. O Ho: 0, 2 = 02 2 versus Ha: 61 2> 022 O Ho: 01 6 2 # 02 2 versus Ha: 012 = 02 O Ho: 01 2 = 024 versus Ha : 01 1 26 02 OH:012 2 202- 5,2 versus Ha: 01 1 2 7 02 OH: 012 6, 2 = 0,2 versus Ha: 61 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 > State the conclusion. O Ho is rejected. There is sufficient evidence to indicate that the variances are different. O Ho is not rejected. There is sufficient evidence to indicate that the variances are different. O Ho is rejected. There is insufficient evidence to indicate that the variances are different. Ho is not rejected. There is insufficient evidence to indicate that the variances are different. What is the approximate p-value for the test? Op-value o, 2? Test using a = 0.05. State the null and alternative hypotheses. ,2 versus Ha : 01 2 > 622 OH :0 2 > 0 2 5,2 versus Ha: 012 02 O Ho: 0 1 2 > 02 2 versus Ha: 012 = 02 OH: 0 2 = 0, 2 versus Ha: 0 12 > 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 > State the conclusion. O H is not rejected. There is insufficient evidence to indicate that o 2 > 6, 2. O Ho is not rejected. There is sufficient evidence to indicate that o z > oz O Ho is rejected. There is sufficient evidence to indicate that of > O Ho is rejected. There is insufficient evidence to indicate that of o, (b) Find the approximate p-value for the test. p-value 02 OH: 012 2
62 OH: 1 2 = 0,2 versus Ha: 012 # 02 O HO : 014 = 2 = 022 versus Ha: 012 State the conclusion. O Ho is rejected. There is sufficient evidence to indicate that o 2 differs from oz O Ho is rejected. There is insufficient evidence to indicate that o 2 differs from oz2. Ho is not rejected. There is insufficient evidence to indicate that of differs from oz. O Ho is not rejected. There is sufficient evidence to indicate that of differs from ozz (b) Find the approximate p-value for the test. O p-value
