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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
Using a linear regression model for prediction beyond the range of observed data can lead to unreliable results due to the potential for extrapolation errors. Since the recorded temperatures do not reach 24 °C, predictions made for this temperature are not based on actual observation and may not accurately reflect the relationship between and .
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 continuous variables, in this case, the daily mean windspeed and daily mean temperature . A positive value indicates a positive correlation, while a negative value indicates a negative correlation.
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 the null hypothesis be (no correlation), and the alternative hypothesis be (positive correlation). We will use the calculated correlation coefficient . The critical value for a one-tailed test at the 5% significance level with 7 degrees of freedom is 0.5822. Since is greater than the critical value, we reject and conclude that 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
Higher ar{T} suggests a location overseas and not near Perth due to lower wind speeds which indicates it is not close to the sea. Therefore, based on the data provided, Beijing could be an appropriate suggestion since it aligns with the higher mean temperature and is located in an area away from the ocean.