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1With reference to Exercise 11.3 on page 398, {a} evaluate 52; {5) construct a 99% condence interval for u; {c} construct a 93% condence interval for 161. 11.3 The amounts of a chemical compound vthat dissolved in we grams otvvater at various temperatures I were recorded as follows: I {OC} 1v {grams} o s s s 15 12 1o 14 so 25 21 24 45 31 33 25 so 44 35 4s 75 45 51 44 {a} Find the equation of the regression line. {5) Graph the line on a scatter diagram. {c} Estimate the amount Df chemical that Will dissolve in 100 grams of water at 5C!\" C. Test the hypothesis that ,8\". = 15 in Exercise 11.3 on page 399 against the alternative that 5o s 15. Use a (105 level of signirmance. 11.3 A mathematics plaoement test is given to all entering freshmen at a small college. A student who receives a grade below 35 is denied admission to the regular mathematics course and placed in a remedial class. The placement test scores and the nal grades for 20 students who took the regular course were reoorded. {a} PM a scatter diagram. {on} Find the equation of the regression line to predict course grades from placement test scores. {c} Graph the line on the scalter diagram. {d} If ED is the minimum passing grade, below which placementtest score should students in the future DE UEHiEU admission 10 this EDUFSE? Placement Test Course Grade 51] 53 35 41 35 51 41] 55 55 53 55 35 35 l 1 51] TD t] 73 35 59 9|] 54 Test the hypothesis that 51 = e in Exercise 11.9 on page 399 against the alternative that p1 e 5. Use a [1525 level of signieanoe. 11.5 A study was made by a retail merchant to determine the relation between weekly advertising expenditures and sales. Advertising Costs (3} Sales ($) 40 3B5 20 400 25 395 2B 355 30 4'35 50 440 4'3 49!] 2D 42D 50 550 4'3 525 25 480 50 510 {3} Plot a scatter diagram. to} Find the equation of the regression line to predict weekly sales from advertising expenditures. to} Estimate the weekly sales when advertising oosts are $35. {d} Plot the residuals versus advertising costs. Comment. \fWith reference to Exercise 11.5 on page 355, use the value of 32 found in Exercise 11.15ia} to compute {a} a 95% condence interval forthe mean shear resistanoe when x = 24.5; {h} a 55% prediction interval for a single predicted value of the shear resistance when x = 24.5. 11.6 In a certain tvpe of metal test specimen, the normal stress on a specimen is known to tie functionallyr related to the shear resistance. The following is a set of coded experimental data on the two variables: Normal Stress, :1: Shear Resistance, gr 26.3 26. 5 25.4 2?. 3 23.3 24. 2 23.6 2?. 1 2727' 23. 6 23.3 25. 3 24.? 26. 3 23.1 22. 5 26.3 21. T 2T.4 21.4 22.6 25.3 25.6 24. 3 {a} Estimate the regression line pY|x = 5d + 51x. {6} Estimate the shear resistance for a normal stress of 24.5. Using the value ofs2 round in Exercise 11.1?[a}, graph the regression line and the 95% condence bands for the mean response p'r'pr for the data of Exercise 11.5 on page 355. 11.1?r With reference to Exercise 11.5 on page 398, {a} evaluate 52; {h} construct a 95% confidence interval for u; {c} construct a 95% condence interval for 151. 11.5 .lftstudy.r was made on the amount of converted sugar in a certain process at various temperatures. The data were coded and recorded as follows: Temperature, 3 Converted Sugar, 3; 1.9 8.1 1.1 18 1.2 8.5 1.3 9.8 1.4 9.5 1.5 8.9 1.8 8.5 1.? 19.2 1.8 9.3 1.9 9.2 2.9 19.5 {a} Estimate the linear regression line. {5} Estimate the mean amount of converted sugar produced when the coded temperature is 1.?5