#6 (use the following to solve a, b, and c below) The Leaning Tower of Pisa is an architectural wonder. Engineers concerned about the tower's stability have done extensive studies on its increasing tilt. The following table shows how the lean has changed in excess of 2.9 meters by year since 1975. A regression analysis was run on this data, and the results from Excel are shown below. ANOVA df Regression Residual Total Intercept Year SS MS F 1 15804.48 15804.48 904.1198 11 192.2857 17.48052 12 15996.77 Coefficients Standard Error t Stat P-value -61.12088 25.12982 -2.432205 0.033279 9.318681 0.309914 30.06858 6.5E-12 Significance F 0.000000000007 Lower 95% Upper 95% Lower 95.0% Upper 95.0% -116.4312367 -5.810522 -116.4312 -5.810522 8.636564768 10.0008 8.636565 10.0008 a) What would Ho and Ha be to show whether the regression line is useful? b) What is the result of the significance test tied to the regression line? Use = 0.05. SOLVE AND INTERPRET CLEARLY AND THOROUGHLY. c) What is the equation of the regression line? (if it in fact exists) 7) From a, b, c and d below, circle the statement that is actually valid. a) A significance test is important because it proves without a shadow of a doubt that an outcome, ie result, is real and will never be wrong. b) Rejecting the null hypothesis means that the outcome of the significance test should be repeatable under similar circumstances, ie experimental conditions. c) If a p-value is very large, it means that the result of the significance test was highly likely, therefore under similar circumstances, a similar result can also be repeatedly achieved. d) The confidence level of a confidence interval indicates how often the random quantity known as the population mean will be located within a confidence interval. Question #8(use the following to solve a, b, c, d, and e below) An engineer working for a leading electronics firm claims to have invented a process for making longerlasting TV picture tubes. Tests run on 24 picture tubes made with the new process show a mean life of 1,725 hours. Tests run over the last 3 years on a very large number of TV picture tubes made with the old process consistently show a mean life of 1,538 hours and a standard deviation of 85 hours. If you would like to test whether the engineer's work has produced a picture tube that definitely lasts longer, what would be... a) ... the null hypothesis? b) ...the alternative hypothesis? c) ...the test statistic? d) ...the critical value? (Use = 0.05) e) ...the result of the significance test? Note: BE THOROUGH. Do NOT just answer Reject or Fail to Reject. Question #9 Professor Jane Newman teaches an introductory calculus course. She wanted to test the belief that success in her course is affected by high school performance. She collected the randomly selected data listed below and ran an ANOVA test as shown below. The data in the \"High School Record\" table represents performance of the student in Jane's calculus. Anova: Single Factor High School Record Good Fair Poor 90 80 60 86 70 60 88 61 SUMMARY Su m 55 Groups Count Average Variance 52 62 80 73 437 87.4 23.8 7 484 69.1428571 4 117.142857 1 Poor 6 357 59.5 45.5 50 65 5 Fair 93 Good 70 83 ANOVA Source of Variation Between Groups 2162.44285 7 Within Groups a) SS 1025.55714 3 df MS F P-value F crit 2 1081.22142 9 15.8141567 6 0.00020221 4 3.68232034 4 15 68.3704761 9 If we set at 0.05, what would we conclude about the ANOVA test? State the null hypothesis Total 3188 17 and result clearly. Give a reason for your result