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In: Statistics and Probability

The table below shows the average weekly wages​ (in dollars) for state government employees and federal...

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 95​% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is ​$899. The equation of the regression line is y= 1.438x - 37.254

Wages (state) X 731 766 787 822 853 892 928 932 960 983

Wages (federal) Y 1,008 1.065 1,112 1,135 1,198 1,230 1,283 1,310 1,332 1,395

Construct and interpret a 95​% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $899. Select the correct choice below and fill in the answer boxes to complete your choice.

Solutions

Expert Solution

BASIC NOTATIONS AND FORMULAS USED TO CALCULATE PREDICTION INTERVAL FOR Y FOR SPECIFIC VALUES OF X:

  • Identify number of ordered pair in the dataset and Degrees of freedom
  • Use the regression equation and the given x-value to find the point estimate
  • Find the critical value that corresponds to the given level of confidence c.
  • Find the standard error of estimate
  • Find the margin of error
  • Find the left and right endpoints and form the prediction interval.

Left Endpoint

Right Endpoint

Interval

GIVEN:

The equation of regression line y= 1.438x - 37.254

Sample size (n) = 10

Since sample size (n) = 10,

Degrees of freedom

The average weekly wages of state government employees is given to be ​$899.

Thus given the equation of regression line ​ and , the point estimate is,

  

  

The t critical value with 8 degrees of freedom and 95% confidence level is .

STANDARD ERROR:

We know that

           
731 1008 1013.924 -59.24 3509.3776
766 1065 1064.254 0.746 0.5565
787 1112 1094.452 17.548 307.9323
822 1135 1144.782 -9.782 95.6875
853 1198 1189.36 8.64 74.6496
892 1230 1245.442 -15.442 238.4554
928 1283 1297.21 -14.21 201.9241
932 1310 1302.962 7.038 49.5334
960 1332 1343.226 -11.226 126.0231
983 1395 1376.3 18.7 349.69

  

  

  

Using these values, the margin of error

  

  

Using ​ and ,

Left Endpoint

Right Endpoint

Thus the 95% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is ​$899 is given by,

Thus we are 95% confident that when the average weekly wages of state government employees is ​$899, the average weekly wages of federal government employees​ will be between ​ and ​.

orchestra answered 2 years ago
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