Edexcel S3 2003 June — Question 2 8 marks

Exam BoardEdexcel
ModuleS3 (Statistics 3)
Year2003
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicConfidence intervals
TypeCalculate CI from summary stats
DifficultyModerate -0.5 This is a straightforward confidence interval calculation using the normal distribution with a given sample mean and standard deviation. Part (a) requires direct application of the standard formula with z=2.576, while part (b) asks for a simple interpretation when the true mean falls outside the interval. The question is slightly easier than average because it's a routine textbook exercise with no conceptual complications, though it does require knowledge of the appropriate z-value and the assumption that either the population is normal or the CLT applies.
Spec5.05d Confidence intervals: using normal distribution

2. A random sample of 30 apples was taken from a batch. The mean weight of the sample was 124 g with standard deviation 20 g .
  1. Find a \(99 \%\) confidence interval for the mean weight \(\mu\) grams of the population of apples. Write down any assumptions you made in your calculations. Given that the actual value of \(\mu\) is 140 ,
  2. state, with a reason, what you can conclude about the sample of 30 apples.

2. A random sample of 30 apples was taken from a batch. The mean weight of the sample was 124 g with standard deviation 20 g .
\begin{enumerate}[label=(\alph*)]
\item Find a $99 \%$ confidence interval for the mean weight $\mu$ grams of the population of apples. Write down any assumptions you made in your calculations.

Given that the actual value of $\mu$ is 140 ,
\item state, with a reason, what you can conclude about the sample of 30 apples.
\end{enumerate}

\hfill \mbox{\textit{Edexcel S3 2003 Q2 [8]}}