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
Question 7
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=x2−x1y2−y1=17−1450−41=39=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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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.
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.
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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