7. A farmer monitored the amount of lead in soil in a field next to a factory. He took 100 samples of soil, randomly selected from different parts of the field, and found the mean weight of lead to be \(67 \mathrm { mg } / \mathrm { kg }\) with standard deviation \(25 \mathrm { mg } / \mathrm { kg }\).
After the factory closed, the farmer took 150 samples of soil, randomly selected from different parts of the field, and found the mean weight of lead to be \(60 \mathrm { mg } / \mathrm { kg }\) with standard deviation \(10 \mathrm { mg } / \mathrm { kg }\).

1. Test at the \(5 \%\) level of significance whether or not the mean weight of lead in the soil decreased after the factory closed. State your hypotheses clearly.
2. Explain the significance of the Central Limit Theorem to the test in part(a).
3. State an assumption you have made to carry out this test.