(a) Mark ten or more points on each of the scatter graphs below to show an example of the type of correlation named under each graph. (i) Strong positive correlation (ii) Strong negative correlation (iii) No correlation (b) A few days before the Scottish Independence Referendum in September 2014 a YouGov poll estimated the support for the ‘No’ campaign to be 54%. (i) If YouGov sampled 1000 people, find the margin of error. Write your answer as a percentage, correct to one decimal place. (ii) Create a 95% confidence interval for the level of support for the ‘No’ campaign in the population.

Leaving Cert Mathematics Statistics & Data: (a) Mark ten or more points on e

(a) Mark ten or more points on each of the scatter graphs below to show an example of the type of correlation named under each graph - Leaving Cert Mathematics - Question 6 - 2015

Question 6

(a)-Mark-ten-or-more-points-on-each-of-the-scatter-graphs-below-to-show-an-example-of-the-type-of-correlation-named-under-each-graph-Leaving Cert Mathematics-Question 6-2015.png

(a) Mark ten or more points on each of the scatter graphs below to show an example of the type of correlation named under each graph. (i) Strong positive correlatio... show full transcript

Worked Solution & Example Answer:(a) Mark ten or more points on each of the scatter graphs below to show an example of the type of correlation named under each graph - Leaving Cert Mathematics - Question 6 - 2015

Step 1

Mark ten or more points for strong positive correlation

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Answer

To demonstrate a strong positive correlation, select ten points that increase steadily from the bottom left to the top right of the graph. For example, points could be plotted at (1,2), (2,4), (3,5), (4,6), (5,8), (6,9), (7,10), (8,12), (9,14), (10,15).

Step 2

Mark ten or more points for strong negative correlation

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Answer

To illustrate a strong negative correlation, plot ten points that decrease steadily from the top left to the bottom right of the graph. Possible points could include (1,10), (2,8), (3,6), (4,5), (5,3), (6,2), (7,1), (8,0), (9,-2), (10,-4).

Step 3

Mark ten or more points for no correlation

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Answer

For no correlation, select points that do not show any coherent trend. For example, points may be plotted at (1,5), (2,1), (3,4), (4,2), (5,9), (6,0), (7,8), (8,3), (9,6), (10,7) which appear scattered without a pattern.

Step 4

If YouGov sampled 1000 people, find the margin of error.

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Answer

To find the margin of error, use the formula:

$ME = rac{1}{ ext{sqrt}(n)}$

where $n = 1000$ . Therefore,

\approx 0.03162 \\ \text{which converts to 3.2%}.$$

Step 5

Create a 95% confidence interval for the level of support for the ‘No’ campaign in the population.

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Answer

Using the estimated support of 54% and the margin of error found earlier, the confidence interval can be calculated as:

$\hat{p} \pm ME$

This gives us:

$54\% \pm 3.2\%$

So, the interval is approximately:

$50.8\% \leq p \leq 57.2\%$ .

(a) Mark ten or more points on each of the scatter graphs below to show an example of the type of correlation named under each graph - Leaving Cert Mathematics - Question 6 - 2015

Worked Solution & Example Answer:(a) Mark ten or more points on each of the scatter graphs below to show an example of the type of correlation named under each graph - Leaving Cert Mathematics - Question 6 - 2015

Mark ten or more points for strong positive correlation

Mark ten or more points for strong negative correlation

Mark ten or more points for no correlation

If YouGov sampled 1000 people, find the margin of error.

Create a 95% confidence interval for the level of support for the ‘No’ campaign in the population.

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