Question

The table below shows the average weekly wages? (in dollars) for state government employees and federal government employees for 10 years. Construct and interpret a 90% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $847.

The equation of the regression line is ModifyingAbove y=1.527x-117.366 .

Wages (state), x Wages (federal), y

757 1,020

771 1,045

793 1,107

810 1,144

858 1,184

883 1,249

911 1,280

939 1,305

956 1,345

983 1,374

Construct and interpret a

9090?%

prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is

$ 847.$847.

Select the correct choice below and fill in the answer boxes to complete your choice.

?(Round to the nearest cent as? needed.)

A.

There is a 90% chance that the predicted average weekly wages of federal government employees is between

?$_ and $_ given a state average weekly wage of $847.

B.

We can be 90% confident that when the average weekly wages of state government employees is

?$847 the average weekly wages of federal government employees will be between

?$_

and

?$_

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = -117.36629 + 1.5271519 x
Sample size: 10
R (correlation coefficient) = 0.99271231
R-sq = 0.98547774
Estimate of error standard deviation: 15.902542

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	-117.36629	56.989708	? 0	8	-2.0594295	0.0734
Slope	1.5271519	0.065543702	? 0	8	23.299751	<0.0001

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	137288.97	137288.97	542.8784	<0.0001
Error	8	2023.1267	252.89084
Total	9	139312.1

Predicted values:

X value	Pred. Y	s.e.(Pred. y)	90% C.I. for mean	90% P.I. for new
847	1176.1314	5.1823064	(1166.4947, 1185.7681)	(1145.0293, 1207.2335)

Hence

Option A; 1145.03, 1207.23