Photo AI
A meteorologist believes that there is a relationship between the daily mean windspeed, w kn, and the daily mean temperature, t °C - Edexcel - A-Level Maths Statistics - Question 2 - 2017 - Paper 2
Question 2
A meteorologist believes that there is a relationship between the daily mean windspeed, w kn, and the daily mean temperature, t °C. A random sample of 9 consecutive ... show full transcript
Worked Solution & Example Answer:A meteorologist believes that there is a relationship between the daily mean windspeed, w kn, and the daily mean temperature, t °C - Edexcel - A-Level Maths Statistics - Question 2 - 2017 - Paper 2
Step 1
Explain why a linear regression model based on these data is unreliable on a day when the mean temperature is 24 °C
Answer
A linear regression model requires data within the range over which the model is developed. Since 24 °C is outside the observed temperatures in the dataset (which only goes up to around 19.3 °C), any predictions made at this temperature would involve extrapolation, which is inherently unreliable. This is because the relationship established between temperature and wind speed may not hold outside the observed data range.
Step 2
Step 3
Stating your hypotheses clearly test, at the 5% significance level, whether or not the product moment correlation coefficient for the population is greater than zero.
Answer
Let us define the null and alternative hypotheses:
- Null Hypothesis (H₀): ρ = 0 (there is no correlation between windspeed and temperature)
- Alternative Hypothesis (H₁): ρ > 0 (there is a positive correlation between windspeed and temperature)
To test these hypotheses, we use the product moment correlation coefficient value of r = 0.609.
Using a significance level of 5% and referring to a critical value for the correlation coefficient, we find that the critical value for n-2 degrees of freedom (where n = 9) is approximately 0.5822. Since 0.609 is greater than 0.5822, we reject the null hypothesis. There is evidence that the product moment correlation coefficient for the population is greater than zero.
Step 4
Using your knowledge of the large data set, suggest, giving your reason, the location that gave rise to these statistics.
Answer
Given the higher mean temperature (( \bar{T} = 27.2 )) and the lower mean windspeed (( \bar{w} = 3.5 )), it suggests a location that is warmer and potentially not close to the sea, as proximity to water often leads to higher wind speeds. Therefore, a suitable suggestion would be Beijing, as it aligns with these conditions. Other locations such as Jacksonville could be considered if more evidence is provided to justify the choice, particularly regarding higher mean temperatures.