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.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.