An estate agent recorded the price per square metre, $p$ £m², for 7 two-bedroom houses. He then coded the data using the coding $q = \frac{p - a}{b}$, where $a$ and $b$ are positive constants. His results are shown in the table below. $p$ 1840 1848 1830 1824 1819 1834 1850 $q$ 4.0 4.8 3.4 2.4 1.9 3.4 5.0 (a) Find the value of $a$ and the value of $b$. The estate agent also recorded the distance, $d$ km, of each house from the nearest train station. The results are summarised below. $S_d = 1.02 \\ S_q = 8.22 \\ S_q = -2.17$ (b) Calculate the product moment correlation coefficient between $d$ and $q$. (c) Write down the value of the product moment correlation coefficient between $d$ and $p$. The estate agent records the price and size of 2 additional two-bedroom houses, $H$ and $J$. House | Price (£) | Size (m²) -------|-----------|----------- $H$ | 156,400 | 85 $J$ | 172,900 | 95 (d) Suggest which house is most likely to be closer to a train station. Justify your answer.

A-Level Edexcel Maths Statistics Hypothesis Testing: An estate agent recorded the pri

An estate agent recorded the price per square metre, $p$ £m², for 7 two-bedroom houses - Edexcel - A-Level Maths Statistics - Question 2 - 2015 - Paper 1

Question 2

An estate agent recorded the price per square metre, $p$ £m², for 7 two-bedroom houses. He then coded the data using the coding $q = \frac{p - a}{b}$, where $a$ and... show full transcript

Worked Solution & Example Answer:An estate agent recorded the price per square metre, $p$ £m², for 7 two-bedroom houses - Edexcel - A-Level Maths Statistics - Question 2 - 2015 - Paper 1

Step 1

Find the value of $a$ and the value of $b$

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Answer

To find the values of $a$ and $b$ , we can use the provided coding equation:

For the first data point: $q = 4.0 = \frac{1840 - a}{b}$ Rearranging gives us: $1840 - a = 4.0b$ Therefore, $a = 1840 - 4.0b$
For the second data point: $q = 4.8 = \frac{1848 - a}{b}$ Rearranging gives: $1848 - a = 4.8b$ Hence, $a = 1848 - 4.8b$

Now, we can equate the two expressions for $a$ : $1840 - 4.0b = 1848 - 4.8b$ Solving for $b$ gives: $0.8b = 8 \\ b = 10$

Substituting back, $a = 1840 - 4.0(10) = 1840 - 40 = 1800$

Thus, we find: $a = 1800, b = 10$

Step 2

Calculate the product moment correlation coefficient between $d$ and $q$

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Answer

The formula for the product moment correlation coefficient $r$ is:

$r = \frac{S_{dq}}{\sqrt{S_d^2 S_q^2}}$

Given values:

$S_d = 1.02$
$S_q = 8.22$
$S_{dq} = -2.17$

Now, substituting these into the formula: $r = \frac{-2.17}{\sqrt{(1.02^2)(8.22^2)}}$ Calculating yields: $r \approx -0.749$

This indicates a negative correlation between $d$ and $q$ .

Step 3

Write down the value of the product moment correlation coefficient between $d$ and $p$

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Answer

The product moment correlation coefficient between $d$ and $p$ is given as:

$r \approx -0.749$

Step 4

Suggest which house is most likely to be closer to a train station. Justify your answer.

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Answer

To determine which house is closer to the train station, we can examine the price per square metre for both houses.

For House $H$ :

Price: £156,400
Size: 85 m²
Price per m²: $\frac{156400}{85} \approx 1840$

For House $J$ :

Price: £172,900
Size: 95 m²
Price per m²: $\frac{172900}{95} \approx 1820$

Since a higher price per square metre usually indicates that the house is closer to city amenities, including the train station, House $H$ with a higher price per square metre ( $1840$ ) is most likely to be closer to the train station.

An estate agent recorded the price per square metre, $p$ £m², for 7 two-bedroom houses - Edexcel - A-Level Maths Statistics - Question 2 - 2015 - Paper 1

Worked Solution & Example Answer:An estate agent recorded the price per square metre, $p$ £m², for 7 two-bedroom houses - Edexcel - A-Level Maths Statistics - Question 2 - 2015 - Paper 1

Find the value of $a$ and the value of $b$

Calculate the product moment correlation coefficient between $d$ and $q$

Write down the value of the product moment correlation coefficient between $d$ and $p$

Suggest which house is most likely to be closer to a train station. Justify your answer.

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