| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2021 |
| Session | January |
| Marks | 4 |
| Topic | Confidence intervals |
| Type | Calculate CI from summary stats |
| Difficulty | Moderate -0.3 This is a straightforward confidence interval question requiring standard formula application with known σ. Part (a) is routine calculation (z-value × σ/√n), part (b) is simple interpretation, and part (c) tests basic understanding of t vs z distributions. The small sample size and three-part structure add slight complexity, but no problem-solving or novel insight is required—just textbook procedure application. |
| Spec | 5.05d Confidence intervals: using normal distribution |
Alan's journey time to work can be modelled by a normal distribution with standard deviation 6 minutes.
Alan measures the journey time to work for a random sample of 5 journeys. The mean of the 5 journey times is 36 minutes.
\begin{enumerate}[label=(\alph*)]
\item Construct a 95\% confidence interval for Alan's mean journey time to work, giving your values to one decimal place. [2 marks]
\item Alan claims that his mean journey time to work is 30 minutes.
State, with a reason, whether or not the confidence interval found in part (a) supports Alan's claim. [1 mark]
\item Suppose that the standard deviation is not known but a sample standard deviation is found from Alan's sample and calculated to be 6.
Explain how the working in part (a) would change. [1 mark]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Statistics 2021 Q1 [4]}}