The following data Is representative of that reported In an article with x = burner-area liberation rate (MBtu/hr-ftz) and y = NOX emission rate (ppm): X 100 125 125 150 150 200 200 250 250 300 300 350 400 400 y 140 150 170 200 200 330 270 400 420 440 380 600 610 670 (a) Does the simple linear regression model specify a useful relationship between the two rates? Use the appropriate test procedure to obtain Information about the Pvalue, and then reach a conclusion at signicance level 0.01. State the appropriate null and alternative hypotheses. OH:l=0 Ha:10 OHoz10 Ha:51=o V Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t 16 25 .I 0.000 P-value State the conclusion In the problem context. O Fail to reject Ho. There is evidence that the model is useful. 0 Fall to reject Ho. There is no evidence that the model is useful. Reject Ho. There is evidence that the model is useful. 0 Reject H0. There is no evidence that the model is useful. q! (b) Compute a 95% CI for the expected change in emission rate associated with a 10 MBtu/hrl'tZ increase in liberation rate. (Round your answers to two decimal places.) ( -22.06 x , 42.56 x ) ppm Cardiorespiratory tness is widely recognized as a major component of overall physical well-being. Direct measurement of maximal oxygen uptake (VOZmax) is the single best measure of such tness, but direct measurement is time-consuming and expensive. It is therefore desirable to have a prediction equation for VOzmax in terms of easily obtained quantities. Consider the following variables. y = VOZmax (L/min) x1 = weight (kg) X2 = 59"- (Yr) x3 = time necessary to walk 1 mile (min) x4 = heart rate at the end of the walk (beats/min) Here is one possible model for male students, consistent with the information given in the article "Validation of the Rockport Fitness Walking Test in College Males and Females.\" Y= 5.0 + 0.01x1 0.05x2 0.13x3 0.01x4 + 5 a = 0.4 (a) Interpret 191. (9 Holding all other variables constant, a 1 kg increase in weight will result in a 0.01 L/min increase in VOzmax. 0 Holding all other variables constant, a 0.01 kg increase in weight will result in a 1 L/min increase in vozmax. 0 Holding all other variables constant, a 0.01 kg increase in weight will result in a 1 L/min decrease in Vozmax. 0 Holding all other variables constant, a 1 kg increase in weight will result in a 0.01 L/min decrease in Vozmax. J Interpret #3. (9 Holding all other variables constant, a 1 min increase in walk time will result in a 0.13 L/min decrease in Vozmax. 0 Holding all other variables constant, a 0.13 min increase in walk time will result in a 1 L/min decrease in Vozmax. 0 Holding all other variables constant, a 1 min increase in walk time will result in a 0.13 Umin increase in VOZmax. 0 Holding all other variables constant, a 0.13 min increase in walk time will result in a 1 L/min increase in VOzmax. J (b) What is the expected value of Vozmax when weight is 77 kg, age is 23 yr, walk time is 13 min, and heart rate is 130 b/m? 1.63 v L/min (c) What is the probability that Vozmax will be between 1.11 and 2.15 for a single observation made when the values of the predictors are as stated in part (b)? (Round your answer to four decimal places.) .95 X An information-retrieval system has ten storage locations. Information has been stored with the expectation that the long-run proportion of requests for location / is given by p, = (5.5 - |/ - 5.51)/30. A sample of 196 retrieval requests gave the following frequencies for location 1-10, respectively: 5, 15, 23, 25, 37, 31, 32, 12, 10, and 6. Use a chi-squared test at significance level 0.10 to decide whether the data is consistent with the a priori proportions (use the P-value approach). LO USE SALT State the appropriate hypotheses. HO : P 1 = =, P2 = , P3 = - 201 P4 = - 4 5 5 O 30' 30' 1 P5 = - ", P6 30' , P7 = - ' P 8 = - 30' , P9 = = P 10 = 30 H: no pi = Pio O HO : P 1 # ,P. 30' P2 * - 30' P3 * = 3 O' P4 * - 4 15 # - 5 5 4 3 2 30' 30' P8* 30' Pg * - 30' P10 * 1 30 H : all pi's = Pjo OH: P1 = = P2 , P3 = 3 5 5 P5 P6 P7 3 30' P4 -1 P8 - Pg = 2 30' 30' 30 30 30 30 30 30 " P10 =- 30 H : at least one p; # Pjo O Ho: P1 * 30' P2 * 30' 3 - P4 * - 30' P5* 5 5 3 30 30' 6* 30' P7* - 4 30' P8* 30' Pg * 30' P10 # 5 H : at least one p; = Pio Compute the test statistic value. (Round your answer to three decimal places.) X'=