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.
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
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.
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
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.
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
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.
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
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.
97%
117 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
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.
97%
121 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
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.
Join the Leaving Cert students using SimpleStudy...