| Exam Board | OCR |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2012 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Z-tests (known variance) |
| Type | Type I/II errors and power |
| Difficulty | Standard +0.3 This is a straightforward hypothesis testing question covering standard S2 content: stating hypotheses, finding significance level from critical values using normal distribution, defining Type I error, and calculating Type II error probability. All parts follow textbook procedures with no novel problem-solving required. The calculations are routine applications of the normal distribution with given parameters (n=64, σ=0.87), making it slightly easier than average for A-level. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
It is desired to test whether the average amount of sleep obtained by school pupils in Year 11 is 8 hours, based on a random sample of size 64. The population standard deviation is 0.87 hours and the sample mean is denoted by $\bar{H}$. The critical values for the test are $\bar{H} = 7.72$ and $\bar{H} = 8.28$.
\begin{enumerate}[label=(\roman*)]
\item State appropriate hypotheses for the test, explaining the meaning of any symbol you use. [3]
\item Calculate the significance level of the test. [4]
\item Explain what is meant by a Type I error in this context. [1]
\item Given that in fact the average amount of sleep obtained by all pupils in Year 11 is 7.9 hours, find the probability that the test results in a Type II error. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR S2 2012 Q9 [11]}}