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In June 2016 the UK held a referendum on its membership of the EU - Leaving Cert Mathematics - Question 9 - 2017
Question 9
In June 2016 the UK held a referendum on its membership of the EU. Table 1 below summarises the results. | Votes | |---------------------------|... show full transcript
Worked Solution & Example Answer:In June 2016 the UK held a referendum on its membership of the EU - Leaving Cert Mathematics - Question 9 - 2017
Step 1
Write the number of Invalid or blank votes into the table.
Answer
To find the number of Invalid or blank votes, subtract the total of valid votes (Leave + Remain) from the total votes.
Invalid Votes = Total Votes - (Leave + Remain)
Invalid Votes = 33 577 342 - (17 410 742 + 16 141 241)
Invalid Votes = 33 577 342 - 33 551 983
Invalid Votes = 25 359
Thus, the number of invalid or blank votes is 25,359.
Step 2
Write the number who voted to leave the EU as a percentage of the valid votes.
Answer
To find the percentage of voters who voted to leave the EU:
Percentage = (Leave Votes / Valid Votes) × 100
Percentage = (17 410 742 / 33 551 983) × 100
Percentage ≈ 51.89%
Rounding to the nearest percent, approximately 52% of valid votes were to leave the EU.
Step 3
Draw a suitable chart or charts to represent the data in Table 2.
Answer
For visual representation, a bar chart displaying age groups on the x-axis and the percentage of 'Remain' and 'Leave' votes on the y-axis is suitable. Each age group should have two bars representing 'Remain' and 'Leave' percentages, colored differently for clarity.
Step 4
Find the mean of the “Remain” values given in Table 2 and find the mean of the “Leave” values given in Table 2.
Answer
To calculate the mean:
Mean of Remain = (73 + 62 + 52 + 44 + 43 + 40) / 6 = 52.33%
Mean of Leave = (27 + 38 + 48 + 56 + 57 + 60) / 6 = 47.67%
Thus, the mean of the “Remain” values is 52.33% and the mean of the “Leave” values is 47.67%.
Step 5
Explain why the answers to part b(ii) do not accurately reflect the actual outcome of the referendum.
Answer
The means calculated do not represent the actual outcome because they are based on percentages of voters within each age group rather than the overall population of voters. The actual outcome was influenced by the distribution of voters in each age group, which these averages do not account for.
Step 6
Find the margin of error of this survey.
Answer
The margin of error (ME) can be calculated using the formula:
ME = rac{1}{ ext{sqrt{n}}}
Where n is the sample size (1200 in this case).
Thus,
ext{ME} ightarrow 0.0288675 \\ ext{or } 2.88675 ext{%}$$ \ Which rounded gives a margin of error of approximately 3%.Step 7
Create a 95% confidence interval for the proportion of the Irish population who agreed.
Answer
To calculate the confidence interval for the proportion:
The confidence interval can be calculated using:
Where m is the value from the Z-table for a 95% confidence level (≈ 1.96).
Calculating:
This gives:
Thus, the 95% confidence interval for the proportion is approximately (42.51%, 53.83%).
Step 8
Conduct a hypothesis test to test the party’s claim.
Answer
To conduct the hypothesis test, use:
- Null Hypothesis (H0): p = 0.53 (The proportion is 53%)
- Alternative Hypothesis (H1): p ≠ 0.53 (The proportion is not 53%)
Using the sample proportion:
- Calculate the test statistic using: Substituting values:
Solving this leads to a calculated Z-value which can then be compared to the Z-value from the standard normal distribution at 5% significance level. If the calculated Z is beyond the critical Z value, we reject H0.
Conclusion: Based on the calculated Z, if we find it is not significant, we accept H0 and the party’s claim of 53% is not substantiated.