Question

Baseball statisticians studied how often triples (a certain event in a baseball game) occurred in professional games played between 1947 and 2017. A 98 percent confidence interval to estimate the slope of the linear regression line relating the year, x, and the mean number of triples per game, y, yielded (−0.006,−0.002). A check shows that the conditions necessary for inference for the slope of the regression line are met.

Based on the confidence interval, which of the following claims is supported?

A. The mean number of triples per game is between 0.002 and 0.006.
B. The number of triples per game has increased, on average, per year.
C. There is no linear relationship between the mean number of triples per game and year.
D. There is a negative linear relationship between the mean number of triples per game and year.
E. A conclusion cannot be made about the relationship between year and mean number of triples per game because the values are close to 0.

Answer 1

Answer: D. There is a negative linear relationship between the mean number of triples per game and year.

Step-by-step explanation: This claim is supported by the interval. The interval contains plausible values for the slope of the linear regression line relating year and mean number of triples per game. Since all the values in the interval are negative, the interval supports the claim that increases in the year are associated with decreases in the mean number of triples per game.