3 The masses of sweets produced by a machine are normally distributed with mean \(\mu\) grams and standard deviation 1.0 grams. A random sample of 65 sweets produced by the machine has a mean mass of 29.6 grams.
- Find a \(99 \%\) confidence interval for \(\mu\).
The manufacturer claims that the machine produces sweets with a mean mass of 30 grams.
- Use the confidence interval found in part (i) to draw a conclusion about this claim.
- Another random sample of 65 sweets produced by the machine is taken. This sample gives a \(99 \%\) confidence interval that leads to a different conclusion from that found in part (ii). Assuming that the value of \(\mu\) has not changed, explain how this can be possible.