SAT scores: A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 452. Assume the population standard deviation is \( \sigma=115 \). Part: \( 0 / 4 \) Part 1 of 4 (a) Construct a \( 95 \% \) confidence interval for the mean mathematics SAT score for the entering freshman class. Round the answer to the nearest whole number. A \( 95 \% \) confidence interval for the mean mathematics SAT score is \( 429<\mu<475 \). Part: \( 1 / 4 \) Part 2 of 4 (b) If the sample size were 110 rather than 100, would the margin of error be larger or smaller than the result in part (a)? Explain. The margin of error would be \( \square \) (Choose one) , since \( \square \) (Choose one) in the sample size will \( \square \) (Choose one) the standard error. lancer smaller
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Great question! Increasing the sample size generally leads to a smaller margin of error because a larger sample tends to provide more accurate estimates of the population mean. So, if the sample size were increased from 100 to 110, the margin of error would be smaller, as the increased sample size reduces the standard error, making our estimate more precise. Now, let’s get a bit more interesting! Did you know that the concept of confidence intervals dates back to the 1930s? The renowned statistician Jerzy Neyman is credited with the formal introduction of confidence intervals in 1937. His innovative approach transformed the field of statistics and has since played a crucial role in various disciplines, including social sciences, medical research, and economics!
