Edexcel S4 — Question 4 9 marks

Exam BoardEdexcel
ModuleS4 (Statistics 4)
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicConfidence intervals
TypeCI from raw data list
DifficultyStandard +0.3 This is a straightforward small-sample confidence interval question using the t-distribution. Students must calculate sample mean and standard deviation from given summations, find the appropriate t-critical value, construct the interval, state the normality assumption, and make a simple comparison to £650. All steps are routine S4 procedures with no novel problem-solving required, making it slightly easier than average.
Spec5.05d Confidence intervals: using normal distribution

A town council is concerned that the mean price of renting two bedroom flats in the town has exceeded £650 per month. A random sample of eight two bedroom flats gave the following results, £\(x\), per month. 705, 640, 560, 680, 800, 620, 580, 760 [You may assume \(\sum x = 5345\) and \(\sum x^2 = 3621025\)]
  1. Find a 90\% confidence interval for the mean price of renting a two bedroom flat. [6]
  2. State an assumption that is required for the validity of your interval in part (a). [1]
  3. Comment on whether or not the town council is justified in being concerned. Give a reason for your answer. [2]

Question 4:
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Question 4:
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A town council is concerned that the mean price of renting two bedroom flats in the town has exceeded £650 per month. A random sample of eight two bedroom flats gave the following results, £$x$, per month.

705, 640, 560, 680, 800, 620, 580, 760

[You may assume $\sum x = 5345$ and $\sum x^2 = 3621025$]

\begin{enumerate}[label=(\alph*)]
\item Find a 90\% confidence interval for the mean price of renting a two bedroom flat.
[6]

\item State an assumption that is required for the validity of your interval in part (a).
[1]

\item Comment on whether or not the town council is justified in being concerned. Give a reason for your answer.
[2]
\end{enumerate}

\hfill \mbox{\textit{Edexcel S4  Q4 [9]}}