3. It is known from past evidence that the weight of coffee dispensed into jars by machine \(A\) is normally distributed with mean \(\mu _ { \mathrm { A } }\) and standard deviation 2.5 g . Machine \(B\) is known to dispense the same nominal weight of coffee into jars with mean \(\mu _ { B }\) and standard deviation 2.3 g . A random sample of 10 jars filled by machine \(A\) contained a mean weight of 249 g of coffee. A random sample of 15 jars filled by machine \(B\) contained a mean weight of 251 g .

1. Test, at the \(5 \%\) level of significance, whether or not there is evidence that the population mean weight dispensed by machine B is greater than that of machine A .
2. Write down an assumption needed to carry out this test.