Photo AI
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, $y$, i... 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) and (the number of letters in the first name) is negative. This means that as the number of letters in a last name increases, the number of letters in the first name tends to decrease.
Step 2
Using the scatter diagram comment on Marc’s suggestion
Answer
Marc's suggestion is compatible with the scatter diagram, which shows a negative correlation between the number of letters in the last name and the first name. This supports the idea that parents with longer last names tend to choose shorter first names for their children.
Step 3
Use your calculator to find the product moment correlation coefficient
Answer
By calculating the product moment correlation coefficient for the provided data, we find that the correlation coefficient is approximately This indicates a moderate negative correlation between the two variables.
Step 4
Test whether or not there is evidence of a negative correlation
Answer
To test the hypothesis, we set up the following:
- Null hypothesis : (no correlation)
- Alternative hypothesis : (negative correlation)
Using a significance level of 5%, we can compare the calculated correlation coefficient of approximately with the critical value for the given degree of freedom. Since the p-value associated with this correlation coefficient is less than 0.05, we reject the null hypothesis. Thus, 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.