For a random sample of 12 observations of pairs of values (x, y), the product moment correlation coefficient is -0.456 - CIE - A-Level Further Maths - Question 5 - 2013 - Paper 1
Question 5
For a random sample of 12 observations of pairs of values (x, y), the product moment correlation coefficient is -0.456. Test, at the 5% significance level, whether t... show full transcript
Worked Solution & Example Answer:For a random sample of 12 observations of pairs of values (x, y), the product moment correlation coefficient is -0.456 - CIE - A-Level Further Maths - Question 5 - 2013 - Paper 1
Step 1
State both hypotheses (B0 if not ρ used)
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Answer
We begin by defining our null and alternative hypotheses:
Null Hypothesis (H0): ρ = 0 (no correlation between x and y)
Alternative Hypothesis (H1): ρ < 0 (evidence of negative correlation between x and y)
Step 2
State or use correct tabular one-tail r value
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Answer
For a sample size n = 12, the degrees of freedom are df = n - 2 = 10. At the 5% significance level for a one-tailed test, the critical value from the correlation table is approximately -0.497.
Step 3
Valid method for reaching conclusion
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To reach our conclusion, we will compare the calculated correlation coefficient (r = -0.456) with the critical value (-0.497).
Since -0.456 > -0.497, we do not have enough evidence to reject H0.
Step 4
Conclusion
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Answer
At the 5% significance level, we accept the null hypothesis H0. There is no evidence of a negative correlation between the variables x and y.
