Question

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:   
= 25.5+1.35X, SST=1430, SSR=1188.55, and --(X -  ) 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  =22.5 is _________ to __________

A.		53.531 to 56.869
B.		53.819 to 56.581
C.		52.562 to 55.138
D.		54.056 to 56.344

Answer 1

predicted value at X=22 is:1.35*22+25.5=

55.200

standard error of CI=s*√(1/n+(x0-x̅)2/Sxx)=		0.6676
for 95 % CI value of t=		2.0690	(from excel:tinv(0.05,23)
margin of error E=t*std error=		1.3812
lower confidence bound=xo-E=		53.819
Upper confidence bound=xo+E=		56.581

option B is correct