Question

This table represents the avg weekly U.S. dollar wages for state employees and federal employees for 10 years. Construct and interpret a 90% prediction interval for the average weekly wages of federal employees when the avg weekly wages for state employees is $880. Round to nearest cent if needed.

Equation of regression line is y = 1.370x + 34.950

Wages (state), x	703	766	788	820	856	872	926	931	938	970
Wages (federal), y	1029	1064	1103	1152	1194	1253	1273	1301	1326	1398

1) There is 90% chance that predicted avg weekly wages of federal employees is between ($??) and ($??), given a state avg weekly wage of $880.

2) We can be 90% confident that when the avg weekly wages of state employees is $880, the avg weekly wages of federal employees will be between ($??) and ($??)

Answer 1

Q1. The  prediction interval for an individual response when the predictor is is

where

, ,n is the total no of observation and k is the no of variable, = 1.860 is the tabulated t at (n-2) degree of freedom.

Now

calculation for Se is given below in the table

Wages (state), x	Wages (federal), y
703	1029	998.06	957.2836
766	1064	1084.37	414.9369
788	1103	1114.51	132.4801
820	1152	1158.35	40.3225
856	1194	1207.67	186.8689
872	1253	1229.59	548.0281
926	1273	1303.57	934.5249
931	1301	1310.42	88.7364
938	1326	1320.01	35.8801
970	1398	1363.85	1166.2225
			4505.284

90% prediction interval is .

Q2.)

90% Confidence interval is