1.Inspectors investigated a random sample of 10 of the 13 amp fuses manufactured by a certain company. The maximum currents which these 10 fuses carried before blowing had sample mean 13.28 amps. The maximum current (in amps) which fuses of this type can carry is believed to be

normally distributed with mean and standard deviation 0.5. Test the hypothesis that $\displaystyle \mu$= 13

against the alternative $\displaystyle \mu$ not equal to 13.

2.Stoned dates are sold in packets of nominal weight 500 g. It is believed that the weight (in g) of

such packets is normally distributed with mean $\displaystyle \mu$ and standard deviation 9.5. The actual weights

of stoned dates in a sample of 10 packets had sample mean 493 g. After stating both the null and

alternative hypotheses, and specifying any assumptions made, assess the evidence that $\displaystyle \mu$* < *500.