Question

The number of initial public offerings of stock issued in a​ 10-year period and the total proceeds of these offerings​ (in millions) are shown in the table. Construct and interpret a​ 95% prediction interval for the proceeds when the number of issues is 575. The equation of the regression line is ModifyingAbove y with caret equals 31.653 x plus 17 comma 676.059. ​Issues, x 422 462 686 500 497 386 56 64 190 156 ​Proceeds, y 19 comma 165 28 comma 410 42 comma 958 31 comma 242 35 comma 664 36 comma 709 20 comma 503 11 comma 311 30 comma 460 28 comma 559 Construct and interpret a​ 95% prediction interval for the proceeds when the number of issues is 575. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Round to the nearest million dollars as needed. Type your answer in standard form where​ "3.12 million" means​ 3,120,000.)

A. We can be​ 95% confident that when there are 575 ​issues, the proceeds will be between ​$ nothing and ​$ nothing.

B. There is a​ 95% chance that the predicted proceeds given 575 issues is between ​$ nothing and ​$ nothing.

Answer 1

predcited value at X=575:		35876.33
std error prediction interval= s*√(1+1/n+(x0-x̅)2/Sxx)=				7635.1193
for 95 % CI value of t=				2.306
margin of error E=t*std error                            =				17606.617
lower prediction bound=sample mean-margin of error =				18269.72
Upper prediction bound=sample mean+margin of error=				53482.95

A. We can be​ 95% confident that when there are 575 ​issues, the proceeds will be

between 18270 and 53483