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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
Calculate \(S_{fh}\)
Answer
To calculate (S_{fh}), we can use the formula:
Where each (f_i) and (h_i) correspond to the foot lengths and heights from the table. Calculating this gives us:
[ S_{fh} = 23 \cdot 135 + 26 \cdot 144 + 23 \cdot 136 + 22 \cdot 140 + 27 \cdot 134 + 24 \cdot 130 + 20 \cdot 132 + 21 \cdot 130 = 25291 ]
Step 2
Find the equation of the regression line of h on f in the form \(h = a + bf\)
Answer
To find the equation of the regression line, we first need to calculate the values of (a) and (b):
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Calculate the slope (b): [ b = \frac{S_{fh} - \frac{\sum f \cdot \sum h}{n}}{S_{ff}} ] Plugging in the values where (n = 8): [ b = \frac{25291 - \frac{186 \cdot 1085}{8}}{39.5} = \text{Value for b} ]
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Calculate the intercept (a): [ a = \frac{\sum h}{n} - b \cdot \frac{\sum f}{n} ] Plugging in the values: [ a = \frac{1085}{8} - (b \cdot \frac{186}{8}) = \text{Value for a} ]
Thus, the regression equation will be of the form: [h = a + bf]
Step 3
Step 4
Comment on the reliability of your estimate in (c), giving a reason for your answer
Answer
The estimate is reliable as 25 cm is within the range of the foot lengths measured. Since the data is collected from children and reflects their growth patterns, we can conclude that the prediction is reasonable.
Step 5
Give a reason why the equation in (b) should not be used to estimate the teacher's height
Answer
The equation derived in (b) is based on children's growth data and patterns. Applying it to estimate an adult's height, such as the teacher's, would be inappropriate since adults and children have different growth trajectories and the relationship between foot length and height may not hold.