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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, $t^{ ext{C}}$, for 8 weeks during t... 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
Let the null hypothesis be (no correlation) and the alternative hypothesis be (negative correlation). Using a significance level of 5%, the critical value is . Since our computed correlation coefficient is less than , we reject the null hypothesis. This indicates that there is sufficient evidence to suggest a negative correlation between sales figures and average weekly temperature.
Step 2
Suggest a possible reason for this correlation.
Answer
A possible reason for the observed correlation could be that as temperatures rise, people are more inclined to spend time on the beach instead of shopping. This shift in activities could lead to a decrease in clothing sales during warmer weeks.
Step 3
State, giving a reason, whether or not the correlation coefficient is consistent with Tessa’s suggestion.
Answer
The correlation coefficient of is consistent with Tessa's suggestion of a linear regression model. A strong negative correlation indicates that as one variable increases (temperature), the other variable (sales figures) decreases, supporting the idea of an inverse relationship.
Step 4
State, giving a reason, which variable would be the explanatory variable.
Answer
The explanatory variable would be (average weekly temperature) since it is likely influencing the sales figures . As temperature is expected to affect shopping behavior, it serves as the independent variable in this context.
Step 5
Give an interpretation of the gradient of this regression equation.
Answer
The gradient of the regression equation represents the change in weekly sales figures for each degree increase in temperature. Specifically, for every degree rise in temperature, weekly sales are expected to drop by £171. This suggests a significant negative impact of increasing temperature on sales.