Multiple choice

A simple random sample of 1,000 students at a large high school was selected and asked how often they read books outside of school and whether they preferred fiction or nonfiction. The results are shown in the table. Reading Frequency Fiction Nonfiction Total Daily 180 120 300 Weekly 200 250 450 Rarely 100 150 250 Total 480 520 1,000 Based on the survey, 45% of students read weekly. If the margin of error is ±3%, which of the following is the most accurate conclusion?

  1. The percentage of all students who read weekly is exactly 45%.

  2. The percentage of all students who read weekly is between 42% and 48%.

  3. It is impossible for the percentage of all students who read weekly to be less than 40%.

  4. About 3% of students surveyed were incorrectly classified as weekly readers.
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B Correct answer
Explanation

A margin of error of 3% means the true population proportion is likely within 45% ± 3%, which is 42% to 48%.

AI explanation

The margin of error is applied to the sample percentage to create an interval estimate for the entire population. The survey shows that 45 percent of students read weekly, so you subtract and add the 3 percent margin of error to this value. Calculating 45 minus 3 gives 42 percent, and calculating 45 plus 3 gives 48 percent. This means the percentage of all students who read weekly is estimated to be between 42 percent and 48 percent.

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