Inference from Sample Statistics and Margin of Error Flashcards

A school district reports that a random sample of 350 students had a mean math score of 74 with a margin of error of ±5 points. Which of the following best describes the plausible range for the true mean score of all students in the district?

Answer: Between 69 and 79 points

The margin of error of ±5 is subtracted and added to the sample mean of 74, giving a plausible range of 69 to 79.

A sample of 100 households shows an average electricity bill of $145 per month with a margin of error of ±$12. A researcher claims the true average is less than $130. Is this claim consistent with the survey results?

Answer: No, because $130 is below the confidence interval of $133–$157.

The confidence interval runs from $133 to $157; since $130 falls below the lower bound, it is not a plausible value for the population mean.

A random sample of 1,600 voters shows 55% prefer Candidate A, with a margin of error of ±2.5%. Another survey of 400 voters shows 57% prefer Candidate A, with a margin of error of ±5%. Which statement is best supported?

Answer: The larger sample's estimate is more reliable because it has a narrower margin of error.

A larger sample produces a narrower margin of error, making the estimate from 1,600 voters (±2.5%) more precise and reliable than the estimate from 400 voters (±5%).

A health survey of 900 adults estimates that 22% are classified as having high blood pressure, with a margin of error of ±3 percentage points at 95% confidence. What is the range of values consistent with the survey at this confidence level?

Answer: 19% to 25%

The confidence interval is 22% ± 3%, giving a range from 19% to 25%.

Which change to a study design would most directly decrease the margin of error in estimating a population proportion?

Answer: Increasing the sample size from 200 to 800

Increasing sample size directly decreases the margin of error; the other options either increase it, maintain it, or introduce bias without improving precision.

A 95% confidence interval for the proportion of customers satisfied with a product is (0.62, 0.78). What is the sample proportion and the margin of error?

Answer: Sample proportion = 0.70, margin of error = 0.08

The sample proportion is the midpoint: (0.62 + 0.78)/2 = 0.70, and the margin of error is half the width: (0.78 − 0.62)/2 = 0.08.

A 95% confidence interval for the mean commute time in a city is (28 min, 36 min). A city official claims the mean commute time is over 38 minutes. Which statement is most accurate?

Answer: The claim is not supported because 38 falls outside the confidence interval.

Since 38 minutes is outside the confidence interval (28–36 minutes), it is not a plausible value for the true mean, so the official's claim is not supported.