| Exam Board | WJEC |
|---|---|
| Module | Unit 4 (Unit 4) |
| Year | 2019 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Z-tests (known variance) |
| Type | Two-tail z-test |
| Difficulty | Standard +0.3 This is a straightforward applied normal distribution question covering standard A-level statistics content: z-score calculation, sampling distribution of the mean, and hypothesis testing. All parts follow routine procedures with no novel problem-solving required. Part (a) is basic standardization, part (b) applies the Central Limit Theorem in a standard way, and part (c) is a textbook two-tailed hypothesis test. The context is clear and the mathematical demands are typical for S1/S2 level work, making this slightly easier than average. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation5.05a Sample mean distribution: central limit theorem5.05c Hypothesis test: normal distribution for population mean |
A company produces kettlebells whose weights are normally distributed with mean $16$ kg and standard deviation $0.08$ kg.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that the weight of a randomly selected kettlebell is greater than $16.05$ kg. [2]
\end{enumerate}
The company trials a new production method. It needs to check that the mean is still $16$ kg. It assumes that the standard deviation is unchanged. The company takes a random sample of 25 kettlebells and it decides to reject the new production method if the sample mean does not round to $16$ kg to the nearest $100$ g.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the probability that the new production method will be rejected if, in fact, the mean is still $16$ kg. [4]
\end{enumerate}
The company decides instead to use a 5\% significance test. A random sample of 25 kettlebells is selected and the mean is found to be $16.02$ kg.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Carry out the test to determine whether or not the new production method will be rejected. [6]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 4 2019 Q4 [12]}}