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The margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result would reflect the result of a census of the entire population. The margin of error of ±5 mmHg at a 95% confidence level indicates that if the study were repeated multiple times, 95% of the time the true mean systolic blood pressure for the entire population would fall within 5 mmHg above or below the sample mean of 120 mmHg. This results in a confidence interval from 115 mmHg to 125 mmHg. The other options misinterpret the concept of the margin of error and its implications. Problem: In a biostatistical study, a researcher estimates the average systolic blood pressure of a population to be 120 mmHg based on a random sample. The margin of error is reported as ±5 mmHg at a 95% confidence level. Which of the following statements is correct? A) There is a 95% chance that the average systolic blood pressure of the entire population is precisely 120 mmHg. B) There is a 95% chance that the average systolic blood pressure of the entire population is between 115 mmHg and 125 mmHg. C) The standard deviation of the population's systolic blood pressure is 5 mmHg. D) Every individual in the population has a systolic blood pressure within 5 mmHg of 120 mmHg. Answer: E) There is a 95% chance that the average systolic blood pressure of the entire population is between 115 mmHg and 125 mmHg.
