A-Level Edexcel Maths Statistics Statistical Measures: A teacher asked a random sample

A teacher asked a random sample of 10 students to record the number of hours of television, t, they watched in the week before their mock exam - Edexcel - A-Level Maths Statistics - Question 1 - 2013 - Paper 1

Question 1

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A teacher asked a random sample of 10 students to record the number of hours of television, t, they watched in the week before their mock exam. She then calculated t... show full transcript

Worked Solution & Example Answer:A teacher asked a random sample of 10 students to record the number of hours of television, t, they watched in the week before their mock exam - Edexcel - A-Level Maths Statistics - Question 1 - 2013 - Paper 1

Step 1

Find $S_t$ and $S_{tg}$

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Answer

To find $S_t$ , we use the formula:

$S_t = \sum t^2 - \frac{(\sum t)^2}{n}$

Where:

$\sum t^2 = 8702$
$\sum t = 258$
$n = 10$

Now substituting the values:

$S_t = 8702 - \frac{(258)^2}{10} = 8702 - \frac{66564}{10} = 8702 - 6656.4 = 2045.6$

For $S_{tg}$ , we use:

$S_{tg} = \sum tg - \frac{(\sum t)(\sum g)}{n}$

Where:

$\sum tg = 1550.2$
$\sum g = 63.6$

Now substituting the values:

$S_{tg} = 1550.2 - \frac{(258)(63.6)}{10} = 1550.2 - \frac{16476.8}{10} = 1550.2 - 1647.68 = -97.48$ Therefore, we find:

$S_t = 2045.6$
$S_{tg} = -97.48$

Step 2

Calculate, to 3 significant figures, the product moment correlation coefficient between t and g.

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Answer

The product moment correlation coefficient is calculated using the formula:

$r_{tg} = \frac{S_{tg}}{\sqrt{S_t S_g}}$

Now, substituting the values already calculated and given:

$S_{tg} = -90.68$
$S_t = 2045.6$
$S_g = 7.864$

Calculating:

$r_{tg} = \frac{-90.68}{\sqrt{2045.6 \times 7.864}} = \frac{-90.68}{\sqrt{16118.0336}} = \frac{-90.68}{126.9} \approx -0.7149$

To 3 significant figures, this is approximately $-0.715$ .

Step 3

Describe, giving a reason, the nature of the correlation you would expect to find between v and g.

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Answer

The correlation coefficient between t and v is given as -0.753, which indicates a negative correlation. This means as the hours of television watched increase, the grades in the mock exam tend to decrease.

In relation to hours of revision (v), it is reasonable to expect a positive correlation with grades (g) because higher hours of revision typically lead to better performance in exams. Therefore, as students revise more hours, it is expected that their grades will be higher.

A teacher asked a random sample of 10 students to record the number of hours of television, t, they watched in the week before their mock exam - Edexcel - A-Level Maths Statistics - Question 1 - 2013 - Paper 1

Worked Solution & Example Answer:A teacher asked a random sample of 10 students to record the number of hours of television, t, they watched in the week before their mock exam - Edexcel - A-Level Maths Statistics - Question 1 - 2013 - Paper 1

Find $S_t$ and $S_{tg}$

Calculate, to 3 significant figures, the product moment correlation coefficient between t and g.

Describe, giving a reason, the nature of the correlation you would expect to find between v and g.

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