Question

QUESTION 7 3)-7) The mangers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales (in 1,000 $) generated by the broker. They sampled 25 brokers and determine the number of new clients they have enrolled in the last year and the data are partially presented in the table with the following results: y = 25.5+1.35X, SST=1430, SSR=1188.55, and --(x - 2)2-102. Broker Clients (X) Sales (Y) 1 26 60 2 23 57 25 24 59 The 95% confidence interval estimate for the mean sales made by brokers who have brought into the firm 22 new clients. Using X-22.5 is to 53.531 to 56.869 53.819 to 56.581 54.056 to 56.344 52.562 to 55.138

Answer 1

Ans:- Given that - 25.5 +1.35X = 25.5 7 31:35 & sst = 1430 SSR - 1188.55 → SSE = SST-SSR SSE - 1430 - 1188.55 SSE = 241.45 Estimated error yanance Sé = MSE = SSE 241.45 0-2 25-2 10.4978 → Se = 110.4978 Se = 3:24 It's given that SSxx = E(X;- )2 = 102

We know that (100) Crd)go confidence inteoval for the mean response when X=88 ( (8 + n) + tu, & Vit (99-87) SSxx Therefore, The 95% confidence integral estimate the mean sales made by Hookers who have brought into the firm 22 mees D = 22-5 clinits using Here i-a=0.95 Ź X 20.05 D=25 Then talo 1-23 to.os, 23 = 2.068 given, Xg = 22 & 5 = 22.5

.:954. Confidence integral estimated the mean sales made boy brokers is (22-22.5)2 to 102 2 102 25-5+1.35(22) - 2.068(3.24) 125+ 25.5 +385(22) + 2.068(9.24) V75 + (22-22.5)? (55.2 – 6.7000.2060) to 55.2 +6.700(0.2060)) (55.2 - 1.3804 to 55.2 +1-3804) (53.819 to 56.581)

The 954. confidence interval estimate for the mean sales made by bookess who have brought into the firm 22 new clients using ga - 22.5 is 53.819 to 56.584