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.
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Answer
Set the null hypothesis, ( H_0: \rho = 0 ), against the alternative hypothesis, ( H_1: \rho < 0 ). Given the critical value of -0.6215 for a significance level of 5%, we compare it with the calculated correlation coefficient of -0.915. Since -0.915 < -0.6215, we reject the null hypothesis, indicating a significant negative correlation.
Step 2
Suggest a possible reason for this correlation.
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Answer
As temperature increases, people tend to spend more time on the beach and less time shopping. This leads to a decrease in sales in the clothing shop.
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 since it indicates a strong negative correlation. A higher temperature corresponds with lower sales, which aligns with her linear regression model proposal.
Step 4
State, giving a reason, which variable would be the explanatory variable.
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Answer
The variable 't' (average weekly temperature) would be the explanatory variable as sales are likely to depend on temperature.
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 degree rise in temperature, weekly sales drop by £171.
