Question

A 95% confidence interval for the slope of the regression line relating the number of grams of carbohydrates and the number of kilocalories per 100-gram sample of various raw foods is given by (2.505,6.696). The confidence interval is based on a random sample of n raw foods. A check of the conditions for inference on the slope shows they are reasonably met. Which of the following is a correct interpretation of the interval?

A. 95% of all such samples of size n will produce a sample slope between 2.505 and 6.696 for the regression line relating grams of carbohydrates and kilocalories per 100- g sample of various raw foods.
B. The probability is 0.95 that the true slope of the regression line relating grams of carbohydrates and kilocalories per 100-g sample of various raw foods is between 2.505 and 6.696.
C. We are 95% confident that the slope of the regression line for the random sample of n raw foods is between 2.505 and 6.696.
D We are 95% confident that the predicted number of kilocalories per 100-g sample will be between 2.505 and 6.696.
E. We are 95% confident that the true slope of the regression line relating grams of carbohydrates and kilocalories per 100-g sample of various raw foods is between 2.505 and 6.696.

Answer 1

Answer: E. We are 95% confident that the true slope of the regression line relating grams of carbohydrates and kilocalories per 100-g sample of various raw foods is between 2.505 and 6.696.

Explanation:

The interpretation of a 95% confidence interval: A person can be 95% confident that the true population parameter lies in it.

Given: A 95% confidence interval for the slope of the regression line relating the number of grams of carbohydrates and the number of kilocalories per 100-gram sample of various raw foods is given by (2.505,6.696).

Interpretation: We are 95% confident that the true slope of the regression line relating grams of carbohydrates and kilocalories per 100-g sample of various raw foods is between 2.505 and 6.696.

Correct option: E