Which of the following statements about the margin of error is false?
1. Statisticians routinely construct interval estimates by making their point estimate the interval center and creating a range of other possible values, known as the margin of error, below and above the center
2. The margin of error is a half-width of an interval estimate, equal to the difference between the point estimate on the one hand and either the lower or upper limit of the interval on the other hand
3. The unknown parameter is presumed to lie at the center of the interval that point estimate and margin of error create
4. None of the above
To determine which statement about the margin of error is false, let's examine each statement individually:
1. Statisticians routinely construct interval estimates by making their point estimate the interval center and creating a range of other possible values, known as the margin of error, below and above the center.
This statement is true. When constructing interval estimates, statisticians often use the point estimate as the center of the interval and establish a range of other possible values around it, which is referred to as the margin of error.
2. The margin of error is a half-width of an interval estimate, equal to the difference between the point estimate on the one hand and either the lower or upper limit of the interval on the other hand.
This statement is true. The margin of error represents the amount by which the point estimate can vary while still maintaining a certain level of confidence. It is often calculated as the half-width of the interval estimate and measures the difference between the point estimate and either the lower or upper limit of the interval.
3. The unknown parameter is presumed to lie at the center of the interval that the point estimate and margin of error create.
This statement is false. While the point estimate is often used as the center of the interval, the actual value of the unknown parameter is not presumed to lie exactly at the center. Instead, it is believed to fall within the range established by the margin of error.
Since statement 3 is false, the false statement about the margin of error is statement 3.