Photo AI
An educational expert found that the correlation coefficient between the hours of revision and the scores achieved by 25 students in their A-level exams was 0.379 Her data came from a bivariate normal distribution - AQA - A-Level Maths: Mechanics - Question 16 - 2020 - Paper 3
Question 16
An educational expert found that the correlation coefficient between the hours of revision and the scores achieved by 25 students in their A-level exams was 0.379 H... show full transcript
Worked Solution & Example Answer:An educational expert found that the correlation coefficient between the hours of revision and the scores achieved by 25 students in their A-level exams was 0.379 Her data came from a bivariate normal distribution - AQA - A-Level Maths: Mechanics - Question 16 - 2020 - Paper 3
Step 1
State the Null and Alternative Hypotheses
Answer
The null hypothesis (H₀) states that there is no positive correlation between the hours of revision and exam scores, which can be expressed as:
ho = 0 $$ The alternative hypothesis (H₁) suggests that there is a positive correlation, expressed as: $$ H_1: ho > 0 $$Step 2
Compare Given Correlation Coefficient with Critical Value
Answer
The given correlation coefficient is 0.379, and the critical value for the 1% significance level is 0.4622. Since 0.379 is less than 0.4622, we do not reject the null hypothesis.
This indicates that the evidence is insufficient to suggest a positive correlation between the hours of revision and the scores achieved by students.
Step 3
Conclude the Hypothesis Test
Answer
Based on the comparison, we conclude that there is insufficient evidence to support the claim that there is a positive correlation between the hours of revision and the scores achieved in the A-level exams.