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Tessa owns a small clothes shop in a seaside town - Edexcel - A-Level Maths Mechanics - Question 2 - 2018 - Paper 1
Question 2
Tessa owns a small clothes shop in a seaside town. She records the weekly sales figures, £w, and the average weekly temperature, t °C, for 8 weeks during the summer.... show full transcript
Worked Solution & Example Answer:Tessa owns a small clothes shop in a seaside town - Edexcel - A-Level Maths Mechanics - Question 2 - 2018 - Paper 1
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
To test the hypothesis, we state:
- Null hypothesis (H0): ρ = 0 (There is no correlation between temperature and sales figures)
- Alternative hypothesis (H1): ρ < 0 (There is a negative correlation)
Given the product moment correlation coefficient, r = -0.915, we compare this to the critical value of -0.6215 for a 5% level of significance. Since -0.915 < -0.6215, we reject the null hypothesis and conclude that there is a significant negative correlation between 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 because it indicates a strong negative correlation between temperature and sales, supporting the idea that higher temperatures lead to lower sales.
Step 4
Step 5
Give an interpretation of the gradient of this regression equation.
Answer
The gradient of the regression equation, -171, indicates that for each degree rise in temperature, there is an associated decrease of £171 in weekly sales. This demonstrates the strong negative impact of temperature on Tessa's sales figures.