A biologist is studying the behaviour of bees in a hive - Edexcel - A-Level Maths: Statistics - Question 1 - 2016 - Paper 1
Question 1
A biologist is studying the behaviour of bees in a hive. Once a bee has located a source of food, it returns to the hive and performs a dance to indicate to the othe... show full transcript
Worked Solution & Example Answer:A biologist is studying the behaviour of bees in a hive - Edexcel - A-Level Maths: Statistics - Question 1 - 2016 - Paper 1
Step 1
Show that S_hw = 5601
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Answer
To calculate the value of (S_{hw}), we use the formula:
Shw=∑dhw−n∑d∑w
Where:
(\sum dhw = 13833)
(\sum d = 33.6)
(\sum w = 5601)
(n = 7) (the number of data points)
Plugging in the values:
Shw=13833−733.6×5601=5601
Step 2
State, giving a reason, which is the response variable.
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Answer
The response variable is the number of wiggles, (w), since it depends on the distance, (d), of the food source. The number of wiggles indicates how far the source of food is from the hive.
Step 3
Calculate the product moment correlation coefficient for these data.
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Answer
The product moment correlation coefficient (r) is calculated using the formula:
r=(n∑d2−(∑d)2)(n∑w2−(∑w)2)n∑dhw−∑d∑w
Using the provided sums:
(n = 7)
(\sum w^2 = 80.481)
After calculations, we find (r \approx 0.994).
Step 4
Calculate the equation of the regression line of w on d, giving your answer in the form w = a + bd.
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Once calculated,
(b \approx 0.014142) and (a \approx 5.7), leading to the regression equation:
w=5.7+0.014142d
Step 5
Use your regression equation to estimate the average number of wiggles in the corresponding dance.
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Answer
Using the regression equation (w = 5.7 + 0.014142d) for (d = 350):
w=5.7+0.014142×350=7.5(approximately)
Step 6
Comment, giving a reason, on the reliability of your estimate.
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The reliability of the estimate is high since 350 m is within the range of the existing distance data used to create the regression model. However, extrapolation beyond the observed range can lead to less reliable predictions.
