Question

Construct a 90% prediction interval for the price per gallon of milk when 180 billion pounds of milk is

produced. The amounts of milk produced in the United States and the average prices (in dollars) per
gallon of milk for nine years is given below. (Round to four decimal places).

Answer 1

To construct a 90% prediction interval for the price per gallon of milk when 180 billion pounds of milk is produced, we can use linear regression analysis. First, we need to find the regression equation using the given data points. Then, we can substitute the given production value into the equation to find the predicted price. Finally, we can calculate the prediction interval using the standard error and t-value.

Step-by-step explanation:

To construct a 90% prediction interval for the price per gallon of milk when 180 billion pounds of milk is produced, we can use linear regression analysis. First, we need to find the regression equation using the given data points. Then, we can substitute the given production value into the equation to find the predicted price. Finally, we can calculate the prediction interval using the standard error and t-value.

Let's calculate the regression equation using the given data points:

• ($2.20 per gallon, 720 million gallons)
• ($2.00 per gallon, 700 million gallons)
• ($1.80 per gallon, 680 million gallons)
• ($1.60 per gallon, 640 million gallons)
• ($1.40 per gallon, 600 million gallons)
• ($1.20 per gallon, 550 million gallons)
• ($1.00 per gallon, 500 million gallons)

After finding the regression equation, we can substitute 180 billion pounds into it to get the predicted price. Then, we can calculate the prediction interval using the standard error and t-value.