Question

Imagine that the average score on a test was 72%, give or take 6.5%. The point estimate is ________, while the interval estimate is ________.

a. 6.5%; [59, 85]
b. 72%; [65.5, 78.5]
c. 72%; [-65.5, 78.5]
d. 6.5%; [68.5, 75.5]

Answer 1

The point estimate is the single value estimate of a population parameter, in this case, 72%. The interval estimate, which accounts for variability, is the range within we expect the true average to lie, calculated as [65.5, 78.5] by adding and subtracting the margin of error from the point estimate.

Step-by-step explanation:

The question is asking us to provide the point estimate and interval estimate for the average score on a test. In statistical terms, the point estimate refers to a single value given as the estimate of a population parameter, which in this case would be the average test score. The interval estimate, on the other hand, gives a range within which we can confidently say the true average lies, accounting for possible sample variability.

The correct answer is b: The point estimate is 72%; the interval estimate is [65.5, 78.5].

To obtain the interval estimate, we take the point estimate and subtract and then add the margin of error to create a range. For this specific case, we take 72% and add and subtract 6.5% to achieve the interval estimate. So, 72% - 6.5% gives us the lower bound, which is 65.5%, and 72% + 6.5% gives us the upper bound, which is 78.5%. Therefore, the interval estimate is [65.5, 78.5].