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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 consecut... 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
The linear regression model is unreliable for extrapolation beyond the range of the data. Since the highest mean temperature in the sample is 19.3 °C, predicting for a day with a mean temperature of 24 °C involves estimating values outside the observed range, which may not accurately reflect the true relationship between temperature and windspeed.
Step 2
State what is measured by the product moment correlation coefficient.
Answer
The product moment correlation coefficient measures the strength and direction of the linear relationship between two variables, in this case, the daily mean windspeed and the daily mean temperature . It quantifies how closely the data points cluster around a straight line.
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
Hypotheses:
- Null Hypothesis (): (There is no correlation between and )
- Alternative Hypothesis (): (There is a positive correlation between and )
Using a one-tailed test and comparing the calculated correlation coefficient to the critical value of 0.5822 at the 5% significance level, we reject as . This indicates that there is evidence to support a positive correlation between windspeed and temperature.
Step 4
Using your knowledge of the large data set, suggest, giving your reason, the location that gave rise to these statistics.
Answer
The higher mean temperature of 27.2 °C suggests a location that has warmer conditions, likely overseas or not near large bodies of water, as they typically moderate temperature. Hence, a potential location is Beijing, which aligns with the higher wind speed of 3.5 kn and tends to experience such conditions.