You work for a horse farrier. You take a random sample of 75 Quarter Horses and determine that their mean height is 15.2 hands. Which statement is true?
A You conclude that the mean height of all Quarter Horses is close to 15.2 hands.
B You conclude that the height of half of the Quarter Horses is less than 15.2 hands.
C You conclude that the height of half of the Quarter Horses is more than 15.2 hands.
D You conclude that the height of all Quarter Horses is exactly 15.2 hands.
A You conclude that the mean height of all Quarter Horses is close to 15.2 hands.
The correct statement is:
A. You conclude that the mean height of all Quarter Horses is close to 15.2 hands.
By taking a random sample of 75 Quarter Horses and determining their mean height to be 15.2 hands, you can infer that the mean height for all Quarter Horses is likely to be close to 15.2 hands. However, it does not provide information about individual horses' heights or whether half of the Quarter Horses are above or below 15.2 hands, as stated in options B, C, and D.
To answer this question, we need to understand the concept of sampling and generalization.
In this scenario, you took a random sample of 75 Quarter Horses and determined their mean height to be 15.2 hands. Based on this information, let's evaluate each statement:
A. "You conclude that the mean height of all Quarter Horses is close to 15.2 hands."
This statement is reasonable. Since you calculated the mean height based on a random sample, it is likely that the mean height of all Quarter Horses is close to 15.2 hands. However, we cannot say for certain without further analysis.
B. "You conclude that the height of half of the Quarter Horses is less than 15.2 hands."
This statement is not supported by the information provided. The mean height does not provide information about what proportion of the Quarter Horses have a height less than 15.2 hands. To determine this, we would need additional data or conduct a different type of analysis.
C. "You conclude that the height of half of the Quarter Horses is more than 15.2 hands."
Similar to statement B, the mean height does not provide information about what proportion of the Quarter Horses have a height greater than 15.2 hands. We need additional data or a different analysis method to make such a conclusion.
D. "You conclude that the height of all Quarter Horses is exactly 15.2 hands."
This statement is not supported by the information provided. The mean height is calculated based on the sample, and it does not provide information about the individual heights of all Quarter Horses. There could be variation in the heights of individual horses.
Therefore, the correct answer would be A: "You conclude that the mean height of all Quarter Horses is close to 15.2 hands." This conclusion is reasonable based on the information given, but it's important to note that without further analysis, we cannot make definitive statements about all Quarter Horses.