| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2018 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Two-sample confidence interval difference of means |
| Difficulty | Standard +0.3 This is a straightforward two-sample t-test with all summary statistics provided. Part (a) tests basic sampling knowledge, part (b) is a standard hypothesis test requiring calculation of pooled standard error and test statistic, and part (c) asks about the Central Limit Theorem assumption. The question requires routine application of learned procedures with no novel insight or complex multi-step reasoning, making it slightly easier than average. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc5.05c Hypothesis test: normal distribution for population mean |
| Answer | Marks | Guidance |
|---|---|---|
| I don't see any mark scheme content in the text provided. The text "Question 2: 2 | 36 | 56.25 |
I don't see any mark scheme content in the text provided. The text "Question 2: 2 | 36 | 56.25 | 7.29 | 23.04" appears to be data (possibly numerical values or a table) rather than a mark scheme with marking annotations (M1, A1, B1, DM1, etc).
Could you please provide the actual mark scheme content that needs to be cleaned up?\begin{enumerate}
\item Merchandise is sold at concerts. The manager of a concert claims that the mean value of merchandise sold to premium ticket holders is more than $\pounds 6$ greater than the mean value of merchandise sold to standard ticket holders.\\
(a) Given that all the tickets for the next concert have been sold, describe how a stratified sample should be taken at the concert.
\end{enumerate}
The mean value of merchandise sold to a random sample of 60 standard ticket holders at the concert is $\pounds 15$ with a standard deviation of $\pounds 10$.
The mean value of merchandise sold to a random sample of 55 premium ticket holders at the concert is $\pounds 23$ with a standard deviation of $\pounds 8$.\\
(b) Test the manager's claim at the $5 \%$ level of significance. State your hypotheses clearly.\\
(c) For the test in part (b), state whether or not it is necessary to assume that values of merchandise sold have normal distributions. Give a reason for your answer.\\
REA\\
\hfill \mbox{\textit{Edexcel S3 2018 Q2 [13]}}