Question

4. a) The drive-through services times were recorded for 71 randomly selected customers at the In N Out restaurant. Those times had a mean of 195.3 seconds and a standard deviation of 64.2 seconds. Construct a 95% C.I estimate of the population mean b) The drive- through service times were recorded for 81 randomly selected costumers at Wendy's restaurant. Those times had a mean of 132.8 seconds and a standard deviation of 54.6 seconds. Construct a 95% confidence interval estimate of the population mean c) Use parts a) and b) to determine if IN N Out drive through wait time is better than Wendy's. Explain

​​​​​​​Please show hand written work for everything including formulas etc.

Answer 1

ay Mean drive through service Standard deviation = 64.2 time=195-35ees a M= populu meah. Statistic.used a vuln-M=T uth, ie 't -distribution with. Now Tu tri ie 't - nol degrees of freedom. Heen=71. ; 2=0.05 From the tressy of confidence internal. P[tmija & Tu 19-M) < tunje] =12 =) p/ 7 - 4 tuning e Me thtwise ] == d. 957. CI is [ * turisĘand one twoją] the from t-table: +70;0.025 - 1.9944. .5-2 timer; = 1953 - 542.11.99wu - 195.3 - 15. 1956 = 180.104 at man zuri się = 195-3 + C4.2 x 1.9944 -) 195.34 15.1956= 210.495. 95% CI is [ 18o. 104, 210.495] 71 VAI

by Similarly for hire n = 132.8sce. d=54-6 ; n = 81.3250005 : 95% CI is given by [x - 1 twigs with train] ☆ from t- table too.jo.025 = 1.9900 132.8 - 54€ x 1.9900 Vot :9132.8-12-07 2 = 120.727 het en time, į = 132.8+ Share yo 9.900 = 132.8712-07 2 = 144.872. 95% CI is [120.727, 144.872] c) Wendy's has betten drive through. wait time than that of. IN N out drive as the. average wait time of wendy's rarges from t 120.727 to o 144.972.. Which. is wouj ten than IN N out drive. Also me rength of interval is also small.