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2 marksSources of Data

CAPE Applied Mathematics Unit 1 · 2021 · Paper 2 · Question 1(a)

Sampling methods comparison and selection of applicants for a competition.

State ONE similarity and ONE difference between a stratified random sample and a quota sample.

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Other parts of this question

  1. 1(b)(i)Identify the sampling method T: selecting equal numbers of male and female contestants, even though there are twice as many female applicants as male…[1 mark]
  2. 1(b)(ii)Identify the sampling method U: grouping applicants by age and selecting contestants at random from within each group in proportion to the number of applicants…[1 mark]
  3. 1(b)(iii)Identify the sampling method V: assigning a unique number from 001 to 500 to each applicant and using random numbers to select the contestants.[1 mark]
  4. 1(b)(iv)Identify the sampling method W: selecting a contestant randomly from among the first k applicants on a numbered list, then selecting every kth applicant on the…[1 mark]
  5. 1(b)(v)Identify by letter the sampling method among T, U, V, and W that would result in a sample that is MOST representative of the 500 applicants.[1 mark]
  6. 1(b)(vi)If sampling method U is used, 4 of the 20 contestants selected from the 500 applicants are over 50 years old. Determine the total number of applicants who are…[2 marks]
  7. 1(b)(vii)Using a random sampling numbers table, starting at row 1, column 3 with 36 and moving from left to right along the row, list the first FIVE numbers selected to…[3 marks]
  8. 1(b)(viii)Calculate the value of k in sampling method W when selecting 20 contestants from 500 applicants.[2 marks]
  9. 1(c)(i)Complete the cumulative frequency row in the provided table.[1 mark]
  10. 1(c)(ii)On the grid provided, draw a cumulative frequency curve to represent the data in the table, using a scale of 2 cm to represent 10 minutes on the x-axis and 2…[4 marks]
  11. 1(c)(iii)Using your cumulative frequency curve, estimate the median time taken to complete the reading assignment.[1 mark]
  12. 1(c)(iv)Using your cumulative frequency curve, estimate the interquartile range.[3 marks]
  13. 1(c)(v)Using your cumulative frequency curve, estimate the proportion of children who took less than 35 minutes to complete the reading assignment.[2 marks]

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