Tessa owns a small clothes shop in a seaside town - Edexcel - A-Level Maths: Mechanics - 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.
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Worked Solution & Example Answer:Tessa owns a small clothes shop in a seaside town - Edexcel - A-Level Maths: Mechanics - 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.
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Answer
To test the correlation, we set our null hypothesis (H0) as:
H0: There is no negative correlation between sales figures and average weekly temperature (ρ = 0).
And our alternative hypothesis (H1) as:
H1: There is a negative correlation between sales figures and average weekly temperature (ρ < 0).
Using the product moment correlation coefficient of -0.915, we can use a critical value table for a significance level of 0.05 to determine if we can reject the null hypothesis. The critical value for 6 degrees of freedom is approximately -0.707. Since -0.915 < -0.707, we reject H0. Therefore, we conclude there is sufficient evidence to support that the correlation is negative.
Step 2
Suggest a possible reason for this correlation.
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Answer
A possible reason for the negative correlation could be that as the average temperature increases, customers may spend less time in the shop, opting for outdoor activities instead.
Step 3
State, giving a reason, whether or not the correlation coefficient is consistent with Tessa’s suggestion.
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Answer
The correlation coefficient of -0.915 is consistent with Tessa’s suggestion that a linear regression could be used, as it indicates a strong negative linear relationship.
Step 4
State, giving a reason, which variable would be the explanatory variable.
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The explanatory variable would be the average weekly temperature (t), as it is used to explain the variations in weekly sales figures (w).
Step 5
Give an interpretation of the gradient of this regression equation.
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Answer
The gradient of the regression equation (-171) indicates that for every 1°C increase in average weekly temperature, the weekly sales figures are predicted to decrease by £171.
