Question

Problem 4: Errors in medical prescriptions occur and a study examined whether electronic prescribing may help reduce errors. Two groups of doctors used written prescriptions and had similar error rates before the study. One group switched to e-prescriptions while the other continued to use written prescriptions, and error rates were measured one year later. The results are given in the following table. Error No Error Total Electronic 254 3594 3848 Written 1478 2370 3848 a. Find a 99% confidence interval for the difference in the two proportions, P«- Pe, where P. is the proportion of errors using written prescriptions and P. is the proportion of errors using e- prescriptions. Round your answers to three decimal places. (5 points) Note: For a 99% confidence interval z* = 2.576. b. Provide an appropriate interpretation (in the context of this problem) of your 95% confidence interval. (3 points) 2 Dashboard Calendar To Do Notifications Inbox

Answer 1

be the Let no written jize of sample prescription mo 3848 Let re be sample dize of electrono 3848 pulcription De Let pio. is proportion of error wing eloitten prescription pw. 14 78 0 38 409 5634 3848 Let po proportion of wing electronic precription : 254 0 0 66008316 3848 فل errier be for 99% confidente 2* = 2.576 confidence interval This 99% confidence interval for fw to-pe is. (ow-be) z* fw (1-w) + bell-be) no ne

0.0226774811 + 8161808 180 STEL808180 (0.00880337 ) 2.576 + 858 [ 8h8€ + **-1)41676990.0 (689 Sbo ºh88.0-1) heq Sb Oh PE 9.5.2) (918800990.0 he 9560 h 18.0 Eoſ] (9LS-1) F

Thus botas 0-318073181-0.022677411 Lborbe L0-31807318 + 0*2226774811 0.295395699 <pwape 4 0.346750661 To. 295 2pw-pe < 0.341 for zit 95% 1.960 confidence jnterval They ./گو Confidence interval for pwope is?

(piw - Pe) 2 * bio (1 pW) + fe clape) no he 38 4095634-0.066008316) + (-960) 0.38409563461-0.384095634) 0.066008316(1-dºbboc83 + 3848 3848 0.30926981 t (1-960) (0.00880337) 0.30926985 t 0.0172546052x 0.309 + 0-017 twope 20.309 + 0.017 0.326 B 0.309 0.017 0-292 < po-pe a Thus 957 confidence the value for difference proportion lie between 0.292 and 0.326. بازیبا un