The mass of organic cocoa solids in a specific brand of premium chocolate bars, C C\,C grams, is modelled by a normal distribution with mean 115 g and standard deviation 4.8 g.
State the probability that a randomly selected chocolate bar contains exactly 115 g of organic cocoa solids.
Following a maintenance overhaul of the production line, a quality control manager suspects the mean mass of cocoa solids has shifted. A random sample of 25 chocolate bars was tested, and the total mass of cocoa solids in the sample was found to be 2825 g.
Assuming the distribution of the mass of cocoa solids remains normal with a standard deviation of 4.8 g, test at the 5% significance level whether the mean mass of cocoa solids has changed.
A production technician claims that since the null hypothesis was rejected in part (b), any other random sample of 25 bars would also lead to the rejection of the null hypothesis. Comment on the validity of this claim.
209 exam-style questions on CCEA A Level Maths 4.6 Statistical hypothesis testing (A-level only), covering 4.6.1 Statistical hypothesis testing (A-level only), 4.6.2 Statistical hypothesis testing (A-level only), 4.6.3 Statistical hypothesis testing (A-level only), 4.6.4 Statistical hypothesis testing (A-level only), and 4.6.5 Statistical hypothesis testing (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.