Question

when a random sample of first - year college students is surveyed, 38% of these students say they are undecided about what major to pursue in college. the survey is reported to have a 2.8% margin of error at a 95% level of confidence. based on this information, which one of the following interpretations is most accurate? a. for this result to be valid, at least 2.8% of the population must have been included in the sample. b. 95% of the students in the sample gave survey results that are within 2.8% of the true population percentage. c. there is a 2.8% chance that the sample percentage was computed incorrectly. d. the population percentage is guaranteed to be exactly 2.8% higher than the sample percentage. e. the population percentage is very likely to be within 2.8% of the sample percentage.

Explanation:

The margin of error at a certain confidence - level gives a range within which the true population parameter is likely to lie. A 95% confidence level with a 2.8% margin of error means that we are 95% confident that the true population percentage is within 2.8% of the sample percentage. Option A is incorrect as the margin of error is not related to the proportion of the population in the sample. Option B misinterprets the meaning of the margin of error as it's about the population, not the sample results. Option C is wrong as the margin of error is not about the chance of incorrect computation. Option D is incorrect as the population percentage is not guaranteed to be exactly 2.8% higher.

Answer:

E. The population percentage is very likely to be within 2.8% of the sample percentage.