Standard +0.3 This is a straightforward one-sample z-test for a mean with all values provided. Students must state the CLT assumption, set up hypotheses (H₀: μ=4.2, H₁: μ<4.2), calculate z = (4.16-4.2)/(0.25/√100) = -1.6, and compare to critical value -1.645. While it requires correct procedure and interpretation, it's a standard textbook application with no conceptual challenges, making it slightly easier than average.
The mass, in kilograms, of a species of fish in the UK has population mean 4.2 and standard deviation 0.25.
An environmentalist believes that the fish in a particular river are smaller, on average, than those in other rivers in the UK.
A random sample of 100 fish of this species, taken from the river, has sample mean 4.16 kg.
Stating a necessary assumption, test at the 5% significance level whether the environmentalist is correct. [8]
The mass, in kilograms, of a species of fish in the UK has population mean 4.2 and standard deviation 0.25.
An environmentalist believes that the fish in a particular river are smaller, on average, than those in other rivers in the UK.
A random sample of 100 fish of this species, taken from the river, has sample mean 4.16 kg.
Stating a necessary assumption, test at the 5% significance level whether the environmentalist is correct. [8]
\hfill \mbox{\textit{OCR H240/02 2023 Q10 [8]}}