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Tessa owns a small clothes shop in a seaside town - Edexcel - A-Level Maths Statistics - Question 2 - 2018 - Paper 2
Question 2
Tessa owns a small clothes shop in a seaside town. She records the weekly sales figures, £w, and the average weekly temperature, °C, for 8 weeks during the summer. T... show full transcript
Worked Solution & Example Answer:Tessa owns a small clothes shop in a seaside town - Edexcel - A-Level Maths Statistics - Question 2 - 2018 - Paper 2
Step 1
Stating your hypotheses clearly and using a 5% level of significance, test whether or not the correlation between sales figures and average weekly temperature is negative.
Answer
Let:
- Null hypothesis (H0): ρ = 0 (no correlation)
- Alternative hypothesis (H1): ρ < 0 (negative correlation)
Using a significance level of 5%, we compare the product moment correlation coefficient of -0.915 against the critical value of -0.6215. Since -0.915 < -0.6215, we reject the null hypothesis. This indicates a significant negative correlation between weekly sales figures and average weekly temperature.
Step 2
Step 3
State, giving a reason, whether or not the correlation coefficient is consistent with Tessa's suggestion.
Answer
The correlation coefficient of -0.915 is consistent with Tessa's suggestion of a negative correlation. A strong negative correlation implies that as one variable increases (temperature), the other variable (sales) decreases.
Step 4
Step 5
Give an interpretation of the gradient of this regression equation.
Answer
The gradient of the regression equation w = 10 755 - 171l indicates that for every 1°C increase in average weekly temperature, the weekly sales figures are expected to decrease by £171. This reflects the negative impact that rising temperatures have on clothing sales.