The weights of bags of rice, \(X \mathrm {~kg}\), have a normal distribution with unknown mean \(\mu \mathrm { kg }\) and known standard deviation \(\sigma \mathrm { kg }\). A random sample of 100 bags of rice gave a \(90 \%\) confidence interval for \(\mu\) of \(( 0.4633,0.5127 )\).
Without carrying out any further calculations, use this confidence interval to test whether or not \(\mu = 0.5\)
State your hypotheses clearly and write down the significance level you have used.
A second random sample, of 150 of these bags of rice, had a mean weight of 0.479 kg .
Calculate a \(95 \%\) confidence interval for \(\mu\) based on this second sample.