NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Evaluating statistical claims

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A statistical report in Sydney claims that 21 out of every 110 people in a randomly selected sample have experienced a minor adverse reaction to a new medication. The report states this rate is representative of the entire adult population in the city.

What is the exact proportion of people in the sample who experienced a reaction, expressed as a simplified fraction?

Concept illustrations

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Median, mode and range in sorted data. The ordered values are 2,3,3,8,9. The middle value is 3, the most frequent value is 3, and the range is 9 − 2 = 7. The row uses equal spacing, not a number-line scale.23389↑ medianmode 3 range 7
The ordered values are 2,3,3,8,9. The middle value is 3, the most frequent value is 3, and the range is 9 − 2 = 7. The row uses equal spacing, not a number-line scale.
Comparing three category counts. Illustrative category counts: A = 2, B = 4, C = 9. Separate bars compare categories; the vertical scale starts at zero.05102A4B9C5
Illustrative category counts: A = 2, B = 4, C = 9. Separate bars compare categories; the vertical scale starts at zero.

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The sample size is 110 people, and 21 experienced a minor adverse reaction.
  2. The proportion of people who experienced a reaction is calculated as the number of people with reactions divided by the total sample size.
  3. Set up the fraction: 21 / 110.
  4. Find the greatest common divisor (GCD) of 21 and 110 to simplify the fraction.
  5. Factor 21: 3 × 7.
  6. Factor 110: 2 × 5 × 11.
  7. There are no common prime factors between 21 and 110, so the fraction 21/110 is already in its simplest form.
  8. The exact proportion is therefore 21/110.
  9. Verify by checking if 21 and 110 share any common factor greater than 1. The factors of 21 are 1, 3, 7, 21. The factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110. The only common factor is 1.
  10. No further simplification is possible.
  11. The exact proportion of people in the sample who experienced a reaction is 21/110.
  12. This matches the simplified fraction form required.

Reference answer: 21/110

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