Question

A newly installed automatic gate system was being tested to see if the number of failures in 1,000 entry attempts was the same as the number of failures in 1,000 exit attempts. A random sample of eight delivery trucks was selected for data collection. Do these sample results show that there is a significant difference between entry and exit gate failures? Use a = 0.01. Entry failures Exit failures Truck 1 44 45 Truck 2 43 52 Truck 3 51 55 Truck 4 59 59 Truck 5 65 56 Truck 6 52 47 Truck 7 45 55 Truck 8 42 50 picture Click here for the Excel Data File (a) Choose the appropriate hypotheses. Define the difference as Entry - Exit. Ho: Hd = 0 versus Hy: Md 0 Ho: Md 20 versus H1: Hd < 0 Ho: Md so versus Hy: Hd > 0 (b) Find the test statistic tcalc. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.) tcalc (c) Find the critical value tcrit for a = 0.01. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.) terit (d) Find the p-value. (Round your answer to 4 decimal places.)

Answer 1

Here we have Entry failures 44 45 Exit Failures diff Entry-Exit -01 52 -09 -04 43 51 55 0 0 59 59 65 56 09 52 47 05 -10 45 55 50 -08 42 Ediff = -18 a = Edi -18 1) -2.25 ri N 8 Sa= El di-d]2 12-1) ti ll 110-1) 4,11-01+2.252 +1-08+ 2252) - 6.84 (9) Hypothesis Ho: Md =0 Ha: Md # 0 This is a two failed test.

(b) Test stahishics I calc -2.25 6.84118 Salon -F0.930 , Ale0.005 © Critical value de 0.01 degree of freedom (df) = 0+1=8-1=7 40005,77 A critical ? + 3.500 F3.500) 0 13.500 (d) P-value Pvalue at t = 1-0.9301 Pralu = A disf (d, df, tails) = ddist 10.93,7, 2) 0.383323 -103833) Round bo adecimal Decision places Since Pralue> 10.01) 80 fail to reject the null Hypothesis.