Question

13. A random sample is drawn from a population of known standard deviation 11.3. Construct a 90% confidence interval for the population mean based on the information given (not all of the information given need be used). a. n-36, x =105.2, s=11.2 b. n-100, x =105.2, s - 11.2 14. A random sample is drawn from a population of unknown standard deviation. Construct a 99%99% confidence interval for the population mean based on the information given. a. n=49, x 17.1, s=2.1 b. n-169, x =17.1, s=2.1 15. On every passenger vehicle that it tests an automotive magazine measures, at true speed 55 mph, the difference between the true speed of the vehicle and the speed indicated by the speedometer. For 36 vehicles tested the mean difference was -1.2 mph with standard deviation 0.2 mph. Construct a 90% confidence interval for the mean difference between true speed and indicated speed for all vehicles. 16. A random sample is drawn from a normally distributed population of known standard deviation 55. Construct a 99.8% confidence interval for the population mean based on the information given (not all of the information given need be used). a. n-16, x =98, s=5.6 b. n-9, x =98, s -5.6 17. A college athletic program wishes to estimate the average increase in the total weight an athlete can lift in three different lifts after following a particular training program for six weeks. Twenty-five randomly selected athletes when placed on the program exhibited gain of 47.34lb with standard deviation 6.4 lb. Construct a interval for the mean increase in lifting capacity all athletes would experience if placed on the training program. Assume increases among all athletes are normally distributed. 90% confidence a mean

Answer 1

solutions - | 13. Given n=36,- 105.2 ; S, - 11.2 n=100, X2 = 105.2 ; Sq = 11.2 90% confidence interval Z=1.645 [(x - 1) +(SE OR X-x.) [C105.2-105.2 ) +1.645-x [ 11.2211.22 336" 100 (-3.580, 3.580] 14. 5=171;21=49 ; 5,=2.1. 1217.15 ng=169 ;; S2-2.1 991. Confidence interval Z=2.58 (7) - 22 ) + 2(S.E of (F, -X2)) fa7.1-1.1)+2.58 (02:+ (-0.879, 0.879] | 15. p= 36 ; 17 -1.2 S O 2 90.6 confidence interval 2=1645 (a +2412.) (-1.81 1.645 x PC) = (-1.254, -6.145) 16. ni= 16 ; X=98; S=516 n2=9 ; 8=98; 5-5.6 99.8% confidence interval 2=3 (3,-22 ) + 2 (S. E OF 7, -22 ] 169

(-7.000, 7.000) 13. n=25 * = 47:34 52604 90% confidence interval. 2= 12645 (TI 2012. In I (47.347 1.645x6m) (45.234, 49.445).
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