Question

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 3 years ago
Next > < Previous

Related Solutions

This table represents the avg weekly U.S. dollar wages for state employees and federal employees for...
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...
The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Smitten,...
The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Smitten, a perfectly competitive firm that produces children’s mittens in a competitive market. Smitten's Production Costs Quantity (pairs of mittens) Marginal Cost (dollars) Average Total Cost (dollars) 20 $1.60 $1.25 25 2.00 1.40 30 2.45 1.58 35 3.55 1.86 40 4.00 2.13 45 5.50 2.50 50 6.00 2.85 55 8.50 3.36 Instructions: In part a, enter your answer as a whole number. In parts b–d,...
8. The table below shows the weekly marginal cost (MC) and average total cost (ATC) for...
8. The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Buddies, a perfectly competitive firm that produces novelty ear buds in a competitive market. The market price of ear buds is $6.00 per pair. Quantity of Ear buds MC ($) ATC ($) 5 - 9 10 2 5.5 15 2.44 4.48 20 3.56 4.25 25 4.5 4.3 30 5.02 4.42 35 5.96 4.64 40 8.56 5.13 Instructions: In part a, enter your answer as...
The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Smitten,...
The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Smitten, a perfectly competitive firm that produces children’s mittens in a competitive market. Smitten's Production Costs Quantity (pairs of mittens) Marginal Cost (dollars) Average Total Cost (dollars) 20 $1.60 $1.25 25 2.00 1.40 30 2.45 1.58 35 3.55 1.86 40 4.00 2.13 45 5.50 2.50 50 6.00 2.85 55 8.50 3.36 Instructions: In part a, enter your answer as a whole number. In parts b–d,...
The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Smitten,...
The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Smitten, a perfectly competitive firm that produces children’s mittens in a competitive market. Smitten's Production Costs Quantity (pairs of mittens) Marginal Cost (dollars) Average Total Cost (dollars) 10 $1.60 $5.00 15 2.00 4.00 20 2.45 3.61 25 3.55 3.60 30 4.00 3.67 35 5.50 3.93 40 6.00 4.19 45 8.50 4.67 Instructions: In part a, enter your answer as a whole number. In parts b–d,...
complete the mrp table for the "Button" The table below shows the net weekly demand of...
complete the mrp table for the "Button" The table below shows the net weekly demand of Audi Car model. The lead time to receive the door is 2 weeks. In week 0, there are 5 cars and 15 doors in inventory. It is expected to receive 30 reworked doors in week 10 Week 8 9 10 11 12 13 14 15 16 17 Net demand (car) 20 25 40 12 5 32 24 18 16 30 Suppose that driver door...
The table below shows the weekly relationship between output and number of workers for a factory...
The table below shows the weekly relationship between output and number of workers for a factory with a fixed size of plant.Number of Workers Output001502110330044505590666577008725971010705a. Calculate the marginal product of labor. b. At what point do diminishing returns set in? Explain. c. Based on the table above, if the wage rate is $500.00 and the price of output is $5, how many workers should the firm hire?
The following table shows the average stock price, in dollars, of XYZ Corporation in the given...
The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 $43.73 February 2011 $44.23 March 2011 $44.42 April 2011 $45.21 May 2011 $45.92 (a) Find the equation of the regression line. (Let P be the stock price in dollars and t the time in months since January, 2011. Round the regression coefficients to three decimal places.) P(t) =
The table below shows the net weekly demand of Audi Car model. The lead time to...
The table below shows the net weekly demand of Audi Car model. The lead time to receive the door is 2 weeks. In week 0, there are 5 cars and 15 doors in inventory. It is expected to receive 30 reworked doors in week 10. Week 8 9 10 11 12 13 14 15 16 17 Net demand (car) 20 25 40 12 5 32 24 18 16 30 Suppose that driver door has four buttons, and each other door...
The table below shows the net weekly demand of Audi Car model. The lead time to...
The table below shows the net weekly demand of Audi Car model. The lead time to receive the door is 2 weeks. In week 0, there are 5 cars and 15 doors in inventory. It is expected to receive 30 reworked doors in week 10. Week 8 9 10 11 12 13 14 15 16 17 Net demand (car) 20 25 40 12 5 32 24 18 16 30 Complete the following MRP table for the doors: Week 1 2...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT