| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2021 |
| Session | June |
| Marks | 9 |
| Topic | Z-tests (known variance) |
| Type | One-tail z-test (lower tail) |
| Difficulty | Standard +0.3 This is a straightforward one-sample z-test for a mean with known population standard deviation. Students need to set up hypotheses, calculate a test statistic using the standard formula, compare to critical value, and state standard assumptions. The calculations are routine and the context is a textbook application of hypothesis testing with no novel insight required. Slightly easier than average due to being a direct application of a standard procedure. |
| Spec | 5.05a Sample mean distribution: central limit theorem5.05c Hypothesis test: normal distribution for population mean |
The greatest weight $W$ N that can be supported by a shelving bracket of traditional design is a normally distributed random variable with mean 500 and standard deviation 80.
A sample of 40 shelving brackets of a new design are tested and it is found that the mean of the greatest weights that the brackets in the sample can support is 473.0 N.
\begin{enumerate}[label=(\alph*)]
\item Test at the 1% significance level whether the mean of the greatest weight that a bracket of the new design can support is less than the mean of the greatest weight that a bracket of the traditional design can support. [7]
\item State an assumption needed in carrying out the test in part (a). [1]
\item Explain whether it is necessary to use the central limit theorem in carrying out the test. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics 2021 Q3 [9]}}