Standard +0.3 This is a standard two-sample t-test with all summary statistics provided. Students must identify the appropriate test, calculate the pooled variance, compute the test statistic, and compare to critical values. While it requires multiple steps and careful calculation, it follows a routine procedure taught in S3 with no novel insight required, making it slightly easier than average.
5. A scientist monitored the levels of river pollution near a factory. Before the factory was closed down she took 100 random samples of water from different parts of the river and found an average weight of pollutants of \(10 \mathrm { mg } \mathrm { l } ^ { - 1 }\) with a standard deviation of \(2.64 \mathrm { mg } \mathrm { l } ^ { - 1 }\). After the factory was closed down the scientist collected a further 120 random samples and found that they contained \(8 \mathrm { mg } \mathrm { l } ^ { - 1 }\) of pollutants on average with a standard deviation of \(1.94 \mathrm { mg } \mathrm { l } ^ { - 1 }\).
Test, at the \(5 \%\) level of significance, whether or not the mean river pollution fell after the factory closed down.
5. A scientist monitored the levels of river pollution near a factory. Before the factory was closed down she took 100 random samples of water from different parts of the river and found an average weight of pollutants of $10 \mathrm { mg } \mathrm { l } ^ { - 1 }$ with a standard deviation of $2.64 \mathrm { mg } \mathrm { l } ^ { - 1 }$. After the factory was closed down the scientist collected a further 120 random samples and found that they contained $8 \mathrm { mg } \mathrm { l } ^ { - 1 }$ of pollutants on average with a standard deviation of $1.94 \mathrm { mg } \mathrm { l } ^ { - 1 }$.
Test, at the $5 \%$ level of significance, whether or not the mean river pollution fell after the factory closed down.\\
\hfill \mbox{\textit{Edexcel S3 2003 Q5 [11]}}