| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2016 |
| Session | June |
| 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 routine calculations. Part (a) requires setting up hypotheses and performing a textbook t-test procedure, part (b) asks for standard assumptions (normality, independence), and part (c) involves updating sample variance using the formula relating sum of squares to variance. All parts follow predictable S3 patterns with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean5.05d Confidence intervals: using normal distribution |
| \(n\) | \(\bar{x}\) | \(s^2\) | |
| Exercise regularly | 35 | 26.3 | 12.2 |
| Do not exercise regularly | 42 | 24.8 | 10.1 |
A doctor claims there is a higher mean lung capacity in people who exercise regularly compared to people who do not exercise regularly. He measures the lung capacity, $x$, of 35 people who exercise regularly and 42 people who do not exercise regularly. His results are summarised in the table below.
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
& $n$ & $\bar{x}$ & $s^2$ \\
\hline
Exercise regularly & 35 & 26.3 & 12.2 \\
\hline
Do not exercise regularly & 42 & 24.8 & 10.1 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Test, at the 5\% level of significance, the doctor's claim. State your hypotheses clearly.
(6)
\item State any assumptions you have made in testing the doctor's claim.
(2)
The doctor decides to add another person who exercises regularly to his data. He measures the person's lung capacity and finds $x = 31.7$
\item Find the unbiased estimate of the variance for the sample of 36 people who exercise regularly. Give your answer to 3 significant figures.
(4)
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2016 Q5}}