Test Bank For Probability and Statistics for Engineering and the Sciences 8th Edition by Jay L. Devore Chapter 1_16 d. e. f. Upper-tailed test, df = 19, t = 2.539 Upper-tailed test, df = 5, t = 5.25 Two-tailed test, df = 40, t = -4.5 ANS: a. t = 2.15 is between 1.860 and 2.306, so the p-value is between .025 and .05: .025< p-value< .05. b. 2.201 < | -2.52 | < 2.718, so .01 < - p-value < .025 c. 1.341 < | -1.69 | < 1.753, so .05 < P(t < -1.69) < .10. thus a two-tailed p-value is .10 < p-value < .20 d. p-value = .01 e. 4.032 < t = 5.25 < 5.893, so .001 < p-value < .005 f. 3.551 < | -4.5 |, so P(t < -4.5) < .0005. A two-tailed p-value = 2[P(t < -4.5)] < 2(.0005), or p-value < .001. PTS: 1 17. The times of first sprinkler activation for a series of tests with fire prevention sprinkler systems using an aqueous film-forming were (in sec). 28 42 23 28 24 36 31 34 25 28 29 23 25 The system has been designed so that true average activation time is at most 25 sec under such conditions. Does the data strongly contradict the validity of this design specification? Test the relevant hypotheses at significance level .05 using the P-value approach. ANS: The hypotheses to be tested are , and should be rejected if The computed summary statistics are Because at level .05. , the p-value is between .01 and .025, so is rejected PTS: 1 18. A certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 12 hours. A random sample of 18 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data supports the use of a one-sample t test. a. b. c. d. What hypotheses should be tested if the investigator believe a priori that the design specification has been satisfied? What conclusion is appropriate if the hypotheses of part (a) are tested, t = -2.5, and ? What conclusion is appropriate if the hypotheses of part (a) are tested, t = -2, and ? What should be concluded if the hypotheses of part (a) are tested and t = -3.25? ANS: The appropriate hypotheses are a. b. -2.5 < so we would reject The data indicates that the pens do not meet the design specifications. c. -2.0 is not , so we would not reject . There is not enough evidence to say that the pens don’t satisfy the design specifications. Test Bank For Probability and Statistics for Engineering and the Sciences 8th Edition by Jay L. Devore Chapter 1_16