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A teacher took a random sample of 8 children from a class - Edexcel - A-Level Maths Statistics - Question 7 - 2011 - Paper 2
Question 7
A teacher took a random sample of 8 children from a class. For each child the teacher recorded the length of their left foot, f cm, and their height, h cm. The resul... show full transcript
Worked Solution & Example Answer:A teacher took a random sample of 8 children from a class - Edexcel - A-Level Maths Statistics - Question 7 - 2011 - Paper 2
Step 1
Step 2
Find the equation of the regression line of h on f in the form \( h = a + bf \)
Answer
The regression line formula is derived from:
[b = \frac{S_{fh} - \frac{\sum f \sum h}{n}}{S_{ff}}]
Calculating ( b ):
[b = \frac{25291 - \frac{186 \cdot 1085}{8}}{39.5} = 1.639]
Calculating ( a ):
[a = \frac{\sum h}{n} - b \cdot \frac{\sum f}{n}] [a = \frac{1085}{8} - 1.639 \cdot \frac{186}{8} = 64.75]
Thus, the equation of the regression line is: ( h = 64.75 + 1.639f )
Step 3
Use your equation to estimate the height of a child with a left foot length of 25 cm.
Answer
Substituting ( f = 25 ) into the regression equation:
[h = 64.75 + 1.639 \cdot 25]
Calculating the height:
[h = 64.75 + 40.975 = 105.725]
Thus, the estimated height of the child is approximately 106 cm.
Step 4
Comment on the reliability of your estimate in (c), giving a reason for your answer.
Answer
The estimate should be reliable as 25 cm falls within the range of foot lengths recorded in the dataset (20 cm to 27 cm). However, since this is an extrapolation based on a sample of children, if children significantly differ from this range, the estimate may not be as reliable.
Step 5
Give a reason why the equation in (b) should not be used to estimate the teacher's height.
Answer
The equation should not be used to estimate the teacher's height because it is derived from the measurements of children. The relationship between foot length and height may differ between children and adults, leading to an inaccurate estimate for the teacher.