A random sample of 15 days is taken from the large data set for Perth in June and July 1987 - Edexcel - A-Level Maths Statistics - Question 2 - 2020 - Paper 1
Question 2
A random sample of 15 days is taken from the large data set for Perth in June and July 1987.
The scatter diagram in Figure 1 displays the values of two of the varia... show full transcript
Worked Solution & Example Answer:A random sample of 15 days is taken from the large data set for Perth in June and July 1987 - Edexcel - A-Level Maths Statistics - Question 2 - 2020 - Paper 1
Step 1
Describe the correlation.
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Answer
The scatter plot indicates a negative correlation. As the Daily Mean Temperature increases, the values for the other variable tend to decrease, demonstrating an inverse relationship between the two.
Step 2
Using your knowledge of the large data set, (i) suggest which variable is on the y-axis.
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Answer
The variable on the y-axis is likely to be Daily Total Sunshine, as this is typically dependent on temperature.
Step 3
Using your knowledge of the large data set, (ii) state the units that are used in the large data set for this variable.
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The units for Daily Total Sunshine are usually expressed in hours.
Step 4
Carry out a suitable test to investigate Stav's belief at a 5% level of significance. State clearly your hypotheses.
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Null Hypothesis (H0): There is no correlation between Daily Total Sunshine and Daily Maximum Relative Humidity (ρ = 0).
Alternative Hypothesis (H1): There is a correlation between Daily Total Sunshine and Daily Maximum Relative Humidity (ρ ≠ 0).
Step 5
Carry out a suitable test to investigate Stav's belief at a 5% level of significance. State clearly your critical value.
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The critical value for a two-tailed test at a 5% significance level with 30 - 2 = 28 degrees of freedom can be found using a correlation coefficient table. Given r = -0.377, this value is below the critical value of approximately ±0.361.
Step 6
Comment on the number of hours of sunshine you would expect on that day, given your reasoning for your answer.
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Given that the Daily Maximum Relative Humidity at Heathrow was 97%, which indicates high humidity, we can expect the number of hours of sunshine to be lower than average. Humid conditions typically lead to less sunshine due to cloud cover.
