Lee wishes to find out if there is a relationship between a person's age and the time it takes them to complete a puzzle. Lee decides to conduct an experiment. She asks 12 people to complete the puzzle. She records each person's age and the time taken to complete the puzzle. (a) Make one criticism of Lee's method. (b) This scatter diagram shows the results for ten of the people in Lee's experiment. Here are the other two results. Age (years) 47 60 Time (seconds) 21 34 Plot these results on the scatter diagram. (c) What type of correlation is shown in the scatter diagram? (d) Estimate the time it would take a person aged 35 to complete the puzzle. Show your working to justify your answer. (e) Lee says that at least 80% of the 12 people completed the puzzle in under 30 seconds. Show your working to support your answer.

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Lee wishes to find out if there is a relationship between a person's age and the time it takes them to complete a puzzle - OCR - GCSE Maths - Question 4 - 2018 - Paper 1

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Lee wishes to find out if there is a relationship between a person's age and the time it takes them to complete a puzzle. Lee decides to conduct an experiment. She a... show full transcript

Worked Solution & Example Answer:Lee wishes to find out if there is a relationship between a person's age and the time it takes them to complete a puzzle - OCR - GCSE Maths - Question 4 - 2018 - Paper 1

Step 1

Make one criticism of Lee's method.

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Answer

One criticism of Lee's method is that the sample size of 12 people is too small to draw any significant conclusions. A larger, more randomized sample would provide more reliable results.

Step 2

Plot these results on the scatter diagram.

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Answer

To plot the additional results:

For age 47 years, plot a point at (47, 21) in the scatter diagram.
For age 60 years, plot a point at (60, 34).

Ensure that the points are placed accurately within the grid on the scatter diagram.

Step 3

What type of correlation is shown in the scatter diagram?

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Answer

The correlation shown in the scatter diagram is negative, as the trend indicates that as age increases, the time taken to complete the puzzle tends to decrease.

Step 4

Estimate the time it would take a person aged 35 to complete the puzzle. Show your working to justify your answer.

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Answer

To estimate the time for age 35, locate age 35 on the age axis. Draw a line upwards to meet the trend line established by previous points. Use the coordinates where the trend line intersects to estimate the time, which is approximately 12 seconds.

Step 5

Lee says that at least 80% of the 12 people completed the puzzle in under 30 seconds. Show your working to support your answer.

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Answer

To find out if at least 80% completed the puzzle in under 30 seconds:

Calculate 80% of 12 people:

$0.8 imes 12 = 9.6$

Rounding up, we need at least 10 people.

From the recorded data, count how many completed in under 30 seconds. If 10 or more completed in this time, Lee's statement is correct. Otherwise, it is incorrect.

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Lee wishes to find out if there is a relationship between a person's age and the time it takes them to complete a puzzle - OCR - GCSE Maths - Question 4 - 2018 - Paper 1

Worked Solution & Example Answer:Lee wishes to find out if there is a relationship between a person's age and the time it takes them to complete a puzzle - OCR - GCSE Maths - Question 4 - 2018 - Paper 1

Make one criticism of Lee's method.

Plot these results on the scatter diagram.

What type of correlation is shown in the scatter diagram?

Estimate the time it would take a person aged 35 to complete the puzzle. Show your working to justify your answer.

Lee says that at least 80% of the 12 people completed the puzzle in under 30 seconds. Show your working to support your answer.

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