Question

A magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the 1000 respondents, 14% chose chocolate pie, and the margin of error was given as +4 percentage points. Describe what is meant by the statement that "the margin of error was given as 4 percentage points." Choose the correct answer below.

A. The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 14% +4%.
B. The statement indicates that the study is only 4% confident that the true population percentage of people that prefer chocolate pie is exactly 14%.
C. The statement indicates that the interval 14% +4% is likely to contain the true population percentage of people that prefer chocolate pie.
D . The statement indicates that the study is 100% -4% = 96% confident that the true population percentage of people that prefer chocolate pie is 14%.

Answer 1

The margin of error of 4 percentage points suggests that the actual preference for chocolate pie in the adult population is expected to be within the range of 10% to 18% with a certain level of confidence. A lower margin of error offers more precise poll results, while the sampling error defines the range around the reported percentage where the true value is likely to fall.

Step-by-step explanation:

The statement that 'the margin of error was given as 4 percentage points' refers to the statistical range that is expected to contain the true percentage of the population's preference with a certain level of confidence. Specifically, the correct explanation here is C. It means that the poll results, which indicate that 14% of people chose chocolate pie as their favorite, would likely fall within the range of 10% to 18% (14% ±4%) when considering the entire adult population the sample is meant to represent. This margin of error acknowledges that statistical variations could cause the actual percentage to be slightly higher or lower than the 14% observed in the sample.

Lowering the margin of error makes a poll more precise, hence more dependable for making predictions or understanding preferences.

When a sampling error is given as ±3 percent, for instance, it signifies the degree of uncertainty involved in the sample results. If the reported figure is 30% with a sampling error of ±3%, it indicates the true population figure is likely between 27% and 33% with a certain level of confidence.