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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 x and y is negative. This means that as the number of letters in the last name increases, the number of letters in the first name tends to decrease. There appears to be a slight downward trend in the relationship shown in the scatter diagram.
Step 2
Using the scatter diagram comment on Marc’s suggestion, giving a reason for your answer.
Answer
Marc’s suggestion that parents with long last names tend to give their children shorter first names is compatible with the data. The scatter diagram shows a negative correlation, where most of the data points indicate that students with long last names often have shorter first names.
Step 3
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
To test for a negative correlation, we set our hypotheses as follows:
- Null Hypothesis (H0): ρ = 0 (no correlation)
- Alternative Hypothesis (H1): ρ < 0 (negative correlation)
Using a 5% level of significance, we find our critical value. Given the correlation coefficient of approximately -0.545, we can reject the null hypothesis as it falls in the critical region, suggesting that there is indeed evidence of a negative correlation.