Edexcel S4 — Question 6 12 marks

Exam BoardEdexcel
ModuleS4 (Statistics 4)
Marks12
PaperDownload PDF ↗
TopicConfidence intervals
TypeCalculate CI from summary stats
DifficultyStandard +0.3 This is a standard S4 confidence interval question requiring routine application of formulas for single-sample and two-sample t-intervals. Part (a) is straightforward calculation with given statistics. Part (b) requires computing sample statistics from raw sums, then applying the pooled variance formula—all standard procedures with no novel insight needed. Slightly easier than average due to being purely procedural.
Spec2.02g Calculate mean and standard deviation5.05d Confidence intervals: using normal distribution
Brickland and Goodbrick are two manufacturers of bricks. The lengths of the bricks produced by each manufacturer can be assumed to be normally distributed. A random sample of 20 bricks is taken from Brickland and the length, \(x\) mm, of each brick is recorded. The mean of this sample is 207.1 mm and the variance is 3.2 mm².
  1. Calculate the 98\% confidence interval for the mean length of brick from Brickland. [4]
A random sample of 10 bricks is selected from those manufactured by Goodbrick. The length of each brick, \(y\) mm, is recorded. The results are summarised as follows. \(\sum y = 2046.2\) \(\sum y^2 = 418785.4\) The variances of the length of brick for each manufacturer are assumed to be the same.
  1. [(b)] Find a 90\% confidence interval for the value by which the mean length of brick made by Brickland exceeds the mean length of brick made by Goodbrick. [8]
(Total 12 marks) 
Brickland and Goodbrick are two manufacturers of bricks. The lengths of the bricks produced by each manufacturer can be assumed to be normally distributed. A random sample of 20 bricks is taken from Brickland and the length, $x$ mm, of each brick is recorded. The mean of this sample is 207.1 mm and the variance is 3.2 mm².

\begin{enumerate}[label=(\alph*)]
\item Calculate the 98\% confidence interval for the mean length of brick from Brickland. [4]
\end{enumerate}

A random sample of 10 bricks is selected from those manufactured by Goodbrick. The length of each brick, $y$ mm, is recorded. The results are summarised as follows.

$\sum y = 2046.2$    $\sum y^2 = 418785.4$

The variances of the length of brick for each manufacturer are assumed to be the same.

\begin{enumerate}[label=(\alph*)]
\item[(b)] Find a 90\% confidence interval for the value by which the mean length of brick made by Brickland exceeds the mean length of brick made by Goodbrick. [8]
\end{enumerate}

(Total 12 marks)

\hfill \mbox{\textit{Edexcel S4  Q6 [12]}}
This paper (31 questions)
View full paper
Q1 6 Q1 4 Q1 6 Q1 7 Q1 9 Q2 9 Q2 6 Q2 6 Q2 12 Q2 11 Q3 9 Q3 9 Q3 Q3 9 Q3 13 Q4 9 Q4 9 Q4 13 Q4 13 Q4 12 Q5 11 Q5 15 Q5 13 Q5 17 Q6 14 Q6 16 Q6 12 Q6 17 Q7 17 Q7 16 Q7 17