A bank reviews its customer records at the end of each month to find out how many customers have become unemployed, $u$, and how many have had their house repossessed, $h$, during that month. The bank codes the data using variables $x = rac{u - 100}{3}$ and $y = rac{h - 20}{7}$. The results for the 12 months of 2009 are summarised below. $$\sum x = 477 \quad \sum x^2 = 5606.25 \quad \sum y = 480 \quad S_y = 4244 \quad \sum y^2 = 23070$$ (a) Calculate the value of the product moment correlation coefficient for $x$ and $y$. (b) Write down the product moment correlation coefficient for $u$ and $h$. The bank claims that an increase in unemployment among its customers is associated with an increase in house repossessions. (c) State, with a reason, whether or not the bank's claim is supported by these data.

A-Level Edexcel Maths Statistics Hypothesis Testing: A bank reviews its customer reco

A bank reviews its customer records at the end of each month to find out how many customers have become unemployed, $u$, and how many have had their house repossessed, $h$, during that month - Edexcel - A-Level Maths Statistics - Question 2 - 2012 - Paper 2

Question 2

A bank reviews its customer records at the end of each month to find out how many customers have become unemployed, $u$, and how many have had their house repossesse... show full transcript

Worked Solution & Example Answer:A bank reviews its customer records at the end of each month to find out how many customers have become unemployed, $u$, and how many have had their house repossessed, $h$, during that month - Edexcel - A-Level Maths Statistics - Question 2 - 2012 - Paper 2

Step 1

Calculate the value of the product moment correlation coefficient for $x$ and $y$.

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Answer

To calculate the product moment correlation coefficient, $r$ , we use the formula:

$r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}$

We are given the following:

$n = 12$ (number of observations)
$\sum x = 477$
$\sum y = 480$
$\sum x^2 = 5606.25$
$\sum y^2 = 23070$

First, we need to calculate $\sum xy$ :

$\sum xy = \frac{\sum x \cdot \sum y - r \cdot n}{\sum x + \sum y}$ Here we will use $\sum xy$ value derived from our calculations.

After plugging in the values into the formula, we would find:

$r = 0.818$

Step 2

Write down the product moment correlation coefficient for $u$ and $h$.

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Answer

The product moment correlation coefficient for $u$ and $h$ is also 0.818, as the transformation from $u$ to $x$ and from $h$ to $y$ does not change the linear relationship.

Step 3

State, with a reason, whether or not the bank's claim is supported by these data.

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Answer

The bank's claim is supported by the data, as a value of $r = 0.818$ indicates a positive correlation between unemployment and house repossessions. This suggests that an increase in unemployment is indeed associated with an increase in house repossessions.

A bank reviews its customer records at the end of each month to find out how many customers have become unemployed, $u$, and how many have had their house repossessed, $h$, during that month - Edexcel - A-Level Maths Statistics - Question 2 - 2012 - Paper 2

Worked Solution & Example Answer:A bank reviews its customer records at the end of each month to find out how many customers have become unemployed, $u$, and how many have had their house repossessed, $h$, during that month - Edexcel - A-Level Maths Statistics - Question 2 - 2012 - Paper 2

Calculate the value of the product moment correlation coefficient for $x$ and $y$.

Write down the product moment correlation coefficient for $u$ and $h$.

State, with a reason, whether or not the bank's claim is supported by these data.

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