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Marc took a random sample of 16 students from a school and for each student recorded - the number of letters, x, in their last name - the number of letters, y, in their first name - Edexcel - A-Level Maths: Statistics - Question 2 - 2021 - Paper 1
Question 2
Marc took a random sample of 16 students from a school and for each student recorded - the number of letters, x, in their last name - the number of letters, y, in th... show full transcript
Worked Solution & Example Answer:Marc took a random sample of 16 students from a school and for each student recorded - the number of letters, x, in their last name - the number of letters, y, in their first name - Edexcel - A-Level Maths: Statistics - Question 2 - 2021 - Paper 1
Step 1
Describe the correlation between x and y.
Answer
The correlation between the number of letters in the last name (x) and the first name (y) is negative. As the number of letters in the last name increases, the number of letters in the first name tends to decrease, suggesting an inverse relationship.
Step 2
Using the scatter diagram comment on Marc's suggestion.
Answer
Marc's suggestion that parents with long last names tend to give their children shorter first names is compatible with the data and the scatter diagram. The general trend observed in the scatter plot indicates a negative correlation; as the values for x (last name length) increase, the values for y (first name length) decrease. This supports Marc's hypothesis.
Step 3
Use your calculator to find the product moment correlation coefficient between x and y.
Answer
Using the data provided, the product moment correlation coefficient (r) is calculated as follows:
This indicates a moderate negative correlation between the number of letters in the last name and the first name.
Step 4
Test whether or not there is evidence of a negative correlation between the number of letters in the last name and the number of letters in the first name.
Answer
We will set up our hypotheses as follows:
- Null Hypothesis (H0): ρ = 0 (no correlation)
- Alternative Hypothesis (H1): ρ < 0 (negative correlation)
Using a significance level of 5%, we find the critical value for a one-tailed test. The calculated r value of approximately -0.545 is significant enough to reject the null hypothesis, providing evidence of a negative correlation between the number of letters in the last and first names.