| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | F-test and chi-squared for variance |
| Type | F-test then t-test sequential |
| Difficulty | Standard +0.3 This is a standard two-sample inference problem from S4 requiring an F-test for equality of variances followed by a confidence interval for difference in means. While it involves multiple steps and understanding of when to use pooled vs unpooled variance, these are routine procedures covered extensively in S4 with no novel problem-solving required. The conceptual link in part (c) is straightforward. Slightly easier than average due to clear structure and standard application of learned techniques. |
| Spec | 5.05d Confidence intervals: using normal distribution |
| Sample size | Mean | \(s^2\) | |
| Dry feed | 13 | 25.54 | 2.45 |
| Feed with water added | 9 | 27.94 | 1.02 |
A farmer set up a trial to assess whether adding water to dry feed increases the milk yield of his cows. He randomly selected 22 cows. Thirteen of the cows were given dry feed and the other 9 cows were given the feed with water added. The milk yields, in litres per day, were recorded with the following results.
\begin{tabular}{|c|c|c|c|}
\hline
& Sample size & Mean & $s^2$ \\
\hline
Dry feed & 13 & 25.54 & 2.45 \\
\hline
Feed with water added & 9 & 27.94 & 1.02 \\
\hline
\end{tabular}
You may assume that the milk yield from cows given the dry feed and the milk yield from cows given the feed with water added are from independent normal distributions.
\begin{enumerate}[label=(\alph*)]
\item Test, at the 10\% level of significance, whether or not the variances of the populations from which the samples are drawn are the same. State your hypotheses clearly.
[5]
\item Calculate a 95\% confidence interval for the difference between the two mean milk yields.
[7]
\item Explain the importance of the test in part (a) to the calculation in part (b).
[2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q4 [14]}}