The daily consumption of water by households in a specific region, WWW, is modelled by a normal distribution with mean 420 litres and standard deviation 64 litres.
State the probability that the water consumption of a randomly selected household on a given day is not equal to 420 litres.
Environmental policies were introduced to encourage water conservation. Following these changes, a random sample of 36 households was monitored. The total water consumption for this group over a single day was found to be 13,824 13,824\,13,824 litres.
It is assumed that the distribution of daily water consumption remains normal with a standard deviation of 64 litres.
Investigate, at the 10% level of significance, whether the mean daily water consumption has changed.
A local official argues that if a different sample of 36 households had been selected, the conclusion of the hypothesis test in part (b) would definitely be the same. Comment on the validity of this claim.
