| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2011 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | One-sample z-test known variance |
| Difficulty | Standard +0.3 This is a straightforward S3 hypothesis testing question covering standard one-sample t-test procedures, confidence intervals, and sample size calculation. Part (a) is routine hypothesis testing with clear setup, part (b) is direct confidence interval calculation, part (c) requires basic interpretation, and part (d) is a standard sample size problem using normal approximation. The large sample size (n=90) simplifies calculations. All techniques are textbook exercises with no novel insight required, making it slightly easier than average. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean5.05d Confidence intervals: using normal distribution |
Roastie's Coffee is sold in packets with a stated weight of 250 g. A supermarket manager claims that the mean weight of the packets is less than the stated weight. She weighs a random sample of 90 packets from their stock and finds that their weights have a mean of 248 g and a standard deviation of 5.4 g.
\begin{enumerate}[label=(\alph*)]
\item Using a 5\% level of significance, test whether or not the manager's claim is justified. State your hypotheses clearly.
[5]
\item Find the 98\% confidence interval for the mean weight of a packet of coffee in the supermarket's stock.
[4]
\item State, with a reason, the action you would recommend the manager to take over the weight of a packet of Roastie's Coffee.
[2]
\end{enumerate}
Roastie's Coffee company increase the mean weight of their packets to $\mu$ g and reduce the standard deviation to 3 g. The manager takes a sample of size $n$ from these new packets. She uses the sample mean $\bar{X}$ as an estimator of $\mu$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Find the minimum value of $n$ such that P$(|\bar{X} - \mu| < 1) \geq 0.98$
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2011 Q7 [16]}}