Question

In a random sample of 1,000 high school students, 29 percent indicated that they had read the Declaration of Independence at least once, with a margin of error of 4 percent. Based on this information, which of the following statements is true?

a. It is likely that more than 33 percent of the population have read the Declaration of Independence.
b. It is likely that fewer than 25 percent of the population have read the Declaration of Independence.
c. It is likely that between 25 and 33 percent of the population have read the Declaration of Independence.
d. It is likely that 29 percent of the population has read the Declaration of Independence with a four percent chance that the survey results could be incorrect.

Answer 1

Based on the given information, the statement that is true is that it is likely that between 25 and 33 percent of the population have read the Declaration of Independence.

Step-by-step explanation:

To determine which statement is true based on the given information, we need to consider the margin of error. The margin of error indicates the range within which the true population percentage is likely to fall. In this case, the margin of error is 4 percent.

The statement "It is likely that more than 33 percent of the population have read the Declaration of Independence" is not true because the upper limit of the margin of error allows for a maximum percentage of 33 percent plus 4 percent, which is 37 percent. Therefore, statement a is not true.

The statement "It is likely that fewer than 25 percent of the population have read the Declaration of Independence" is also not true because the lower limit of the margin of error allows for a minimum percentage of 29 percent minus 4 percent, which is 25 percent. Therefore, statement b is not true.

The statement "It is likely that between 25 and 33 percent of the population have read the Declaration of Independence" is true because the confidence interval provided by the margin of error falls within this range. Therefore, statement c is true.

The statement "It is likely that 29 percent of the population has read the Declaration of Independence with a four percent chance that the survey results could be incorrect" is not true. The margin of error does not refer to the chance that the survey results are incorrect, but rather the range within which the true population percentage is likely to fall. Therefore, statement d is not true.