The table below shows the average weekly wages (in dollars) for state government

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 98% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $916. The equation of the regression line is y 1.379x +26.830 Wages (state), x Wages (federal), y 704 744 783 804 841 897 924 935 947 972 | 1,002 1,046 ,108 ,148 1,196 1,240 1,285 ,308 1,3311,399 Construct and interpret a 98% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $916. Select the correct choice below and fill in the answer boxes to complete your choice (Round to the nearest cent as needed.) 0 A. There is a 98% chance that the predicted average weekly wages of federal government employees is between $ and $ given a state average , weekly wage of $916 We can be 98% confident that when the average weekly wages of state government employees is $916, the average weekly wages of federal government employees will be between S ( B. and S

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 26.830113 + 1.3793356 x
Sample size: 10
R (correlation coefficient) = 0.99264069
R-sq = 0.98533554
Estimate of error standard deviation: 16.634751

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

Option B; $ 1238.69; $ 1341.91

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 26.830113 51.143721 0 8 0.52460229 0.6141 Slope 1.3793356 0.059493013 0 8 23.184834 <0.0001

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