Edexcel S3 2009 June — Question 6 10 marks

Exam BoardEdexcel
ModuleS3 (Statistics 3)
Year2009
SessionJune
Marks10
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicT-tests (unknown variance)
TypeTwo-sample z-test large samples
DifficultyStandard +0.3 This is a standard two-sample t-test with large sample sizes (n>30), making it straightforward. The question provides all necessary values, requires routine hypothesis setup, calculation of pooled variance/test statistic, and comparison to critical value. Part (b) asks for standard assumptions (normality, independence). While it's a 10-mark question requiring multiple steps, it follows a completely standard template with no conceptual challenges—slightly easier than the average A-level question due to the large samples and formulaic approach.
Spec5.05c Hypothesis test: normal distribution for population mean

The lengths of a random sample of 120 limpets taken from the upper shore of a beach had a mean of 4.97 cm and a standard deviation of 0.42 cm. The lengths of a second random sample of 150 limpets taken from the lower shore of the same beach had a mean of 5.05 cm and a standard deviation of 0.67 cm.
  1. Test, using a 5\% level of significance, whether or not the mean length of limpets from the upper shore is less than the mean length of limpets from the lower shore. State your hypotheses clearly. [8]
  2. State two assumptions you made in carrying out the test in part (a). [2]

The lengths of a random sample of 120 limpets taken from the upper shore of a beach had a mean of 4.97 cm and a standard deviation of 0.42 cm. The lengths of a second random sample of 150 limpets taken from the lower shore of the same beach had a mean of 5.05 cm and a standard deviation of 0.67 cm.

\begin{enumerate}[label=(\alph*)]
\item Test, using a 5\% level of significance, whether or not the mean length of limpets from the upper shore is less than the mean length of limpets from the lower shore. State your hypotheses clearly. [8]

\item State two assumptions you made in carrying out the test in part (a). [2]
\end{enumerate}

\hfill \mbox{\textit{Edexcel S3 2009 Q6 [10]}}