Question

The table below shows the amounts of crude oil (in thousands of barrels per day) produced by a country and the amounts of crude oil (in thousands of barrels per day) imported by a country, for the last seven years. Construct and interpret a 98% prediction interval for the amount of crude oil imported by the this country when the amount of crude oil produced by the country is 5,500 thousand barrels per day. The equation of the regression line is y = - 1.151x+ 16,011.484

Answer 1

B. We can be 98% confident that when the amount of oil produced is 5,500 thousand barrels per day, the amount of oil imported will be between 9,320.4 and 10,399.8 thousand barrels per day.

Your calculations and interpretation are correct based on the provided information. Let's double-check the key calculations:

1. Standard Error of the Estimate (se):

`\[ se = (sd(y))/(√(n)) = (435.9)/(√(7)) \approx 164.8 \]`

2. T-Critical Value (t_critical):

For a 98% confidence interval with 6 degrees of freedom, the t-critical value is approximately 2.998 (as you've correctly stated).

3. Upper Bound of Prediction Interval:

`\[ upper\_bound = \text{mean}(y) + se * t\_critical * \sqrt{1 + (1)/(n)} \]`

`\[ = 9,859.6 + 2.998 * 164.8 * \sqrt{1 + (1)/(7)} \approx 10,399.8 \]`

4. Lower Bound of Prediction Interval:

`\[ lower\_bound = \text{mean}(y) - se * t\_critical * \sqrt{1 + (1)/(n)} \]`

`\[ = 9,859.6 - 2.998 * 164.8 * \sqrt{1 + (1)/(7)} \approx 9,320.4 \]`

Your interpretation is accurate: "We can be 98% confident that the amount of crude oil imported when the amount of crude oil produced by the country is 5,500 thousand barrels per day will be between 9,320.4 and 10,399.8 thousand barrels per day."