| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2011 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Two-sample z-test large samples |
| Difficulty | Standard +0.3 This is a standard two-sample t-test question with straightforward calculations. Part (a) requires routine application of variance formulas from summary statistics. Part (b) is a textbook hypothesis test setup with pooled variance. While it has multiple steps and 13 marks total, it requires no novel insight—just methodical application of S3 procedures that students practice extensively. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean5.05d Confidence intervals: using normal distribution |
| \(\sum x\) | \(\sum x^2\) | Unbiased estimate of mean | Unbiased estimate of variance | |
| Customers shopping without music | 5320 | 392000 | \(\bar{x}\) | \(s^2\) |
| Customers shopping with music | 4140 | 312000 | 69.0 | 446.44 |
A shop manager wants to find out if customers spend more money when music is playing in the shop. The amount of money spent by a customer in the shop is £$x$. A random sample of 80 customers, who were shopping without music playing, and an independent random sample of 60 customers, who were shopping with music playing, were surveyed. The results of both samples are summarised in the table below.
\begin{tabular}{|c|c|c|c|c|}
\hline
& $\sum x$ & $\sum x^2$ & Unbiased estimate of mean & Unbiased estimate of variance \\
\hline
Customers shopping without music & 5320 & 392000 & $\bar{x}$ & $s^2$ \\
\hline
Customers shopping with music & 4140 & 312000 & 69.0 & 446.44 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item Find the values of $\bar{x}$ and $s^2$.
[5]
\item Test, at the 5\% level of significance, whether or not the mean money spent is greater when music is playing in the shop. State your hypotheses clearly.
[8]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2011 Q4 [13]}}