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An economics student wants to find out whether the length of time people spend in education affects the income they earn - Leaving Cert Mathematics - Question 7 - 2012

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An economics student wants to find out whether the length of time people spend in education affects the income they earn. The student carries out a small study. Twel... show full transcript

Worked Solution & Example Answer:An economics student wants to find out whether the length of time people spend in education affects the income they earn - Leaving Cert Mathematics - Question 7 - 2012

Step 1

The last three rows of data have not been included on the scatter plot. Insert them now.

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Answer

From the scatter plot and the correlation coefficient, we can conclude that there is a positive relationship between the years of education and the annual income. The data shows a rough correlation, suggesting that as the number of years spent in education increases, so does the income, albeit with some outliers visible on the plot.

Step 2

Add the line of best fit to the completed scatter plot above.

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Answer

The line of best fit can be added by plotting a linear regression through the data points. This line should ideally minimize the distance between the individual data points and the line itself.

Step 3

Use the line of best fit to estimate the annual income of somebody who has spent 14 years in education.

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Answer

Using the line of best fit, for an individual with 14 years of education, the estimated annual income is approximately £41,000.

Step 4

By taking suitable readings from your diagram, or otherwise, calculate the slope of the line of best fit.

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Answer

By using two data points from the line of best fit, (14, 41) and (17, 50), the slope can be calculated as:

slope=y2y1x2x1=50411714=93=3\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{50 - 41}{17 - 14} = \frac{9}{3} = 3

Step 5

Explain how to interpret this slope in this context.

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Answer

The slope of 3 indicates that for each additional year of education, the annual income increases by £3,000. This suggests a strong positive correlation between education and income.

Step 6

List three possible problems regarding the sample and how it was collected that might make the results of the investigation unreliable.

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Answer

  1. Non-Response Bias: If selected participants do not answer, it may result in skewed data as those who do respond might have a specific profile that differs from those who do not.

  2. Timing of Calls: Conducting surveys in the evenings might exclude certain demographic groups (e.g., those working evening shifts) which can lead to unrepresentative data.

  3. Selection Method: Randomly selecting from the telephone directory might overlook people without landlines or those who do not use their listed numbers, affecting the diversity of the sample.

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