| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Marks | 17 |
| Paper | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | CI from raw data list |
| Difficulty | Standard +0.3 This is a standard S3 confidence intervals and hypothesis testing question covering routine procedures: calculating sample statistics, finding population limits using z-values, constructing a confidence interval, and performing a one-tailed z-test. All parts follow textbook methods with clearly stated conditions (normal distribution, known variance). The calculations are straightforward with no conceptual challenges or novel problem-solving required, making it slightly easier than average for A-level. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation5.05b Unbiased estimates: of population mean and variance5.05c Hypothesis test: normal distribution for population mean5.05d Confidence intervals: using normal distribution |
The weights of tubs of margarine are known to be normally distributed. A random sample of 10 tubs of margarine were weighed, to the nearest gram, and the results were as follows.
$$498 \quad 502 \quad 500 \quad 496 \quad 509 \quad 504 \quad 511 \quad 497 \quad 506 \quad 499$$
\begin{enumerate}[label=(\alph*)]
\item Find unbiased estimates of the mean and the variance of the population from which this sample was taken. [5]
\end{enumerate}
Given that the population standard deviation is 5.0 g,
\begin{enumerate}[label=(\alph*)]
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\item estimate limits, to 2 decimal places, between which 90\% of the weights of the tubs lie, [2]
\item find a 95\% confidence interval for the mean weight of the tubs. [5]
\end{enumerate}
A second random sample of 15 tubs was found to have a mean weight of 501.9 g.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumii}{3}
\item Stating your hypotheses clearly and using a 1\% level of significance, test whether or not the mean weight of these tubs is greater than 500 g. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 Q7 [17]}}