| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics B AS (Further Statistics B AS) |
| Year | 2022 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Central limit theorem |
| Type | Assumptions for inference |
| Difficulty | Moderate -0.3 This is a straightforward application of t-distribution confidence intervals with standard bookwork parts: stating the normality assumption, calculating a confidence interval from given data (8 values, routine arithmetic), and interpreting whether 30 lies within the interval. While it requires multiple steps and understanding of inference concepts, all components are standard textbook exercises with no novel problem-solving or conceptual challenges beyond typical A-level statistics. |
| Spec | 5.05d Confidence intervals: using normal distribution |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | The population of bus journey times must be Normally |
| distributed. | B1 | |
| [1] | 2.4 | Allow ‘the underlying distribution is Normal’ |
| 1 | (b) | DR |
| Answer | Marks |
|---|---|
| 29.37 < μ < 33.78 or 31.575 ± 2.207 | B1 |
| Answer | Marks |
|---|---|
| [7] | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | BC |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (c) | Confidence interval suggests that Beth may be |
| Answer | Marks |
|---|---|
| …since the interval does contain 30 minutes | B1 |
| Answer | Marks |
|---|---|
| [2] | 3.4 |
| 2.2b | Condone ‘Yes’ |
Question 1:
1 | (a) | The population of bus journey times must be Normally
distributed. | B1
[1] | 2.4 | Allow ‘the underlying distribution is Normal’
1 | (b) | DR
Sample mean = 31.575
Sample SD = 2.640
2 .6 4 0
Confidence interval is given by 3 1 .5 7 5 2 .3 6 5
8
29.37 < μ < 33.78 or 31.575 ± 2.207 | B1
B1
M1
M1
B1
M1
A1
[7] | 1.1
1.1
3.4
1.1a
1.1
1.1
1.1 | BC
BC
For general form
For 7 degrees of freedom
For 2.365 Allow SC B1 for 2.447 from 6 dof
T h e i r 2 .6 4 0
For
8
oe
1 | (c) | Confidence interval suggests that Beth may be
correct…
…since the interval does contain 30 minutes | B1
B1
[2] | 3.4
2.2b | Condone ‘Yes’1 Each working day, Beth takes a bus to her place of work. She believes that the mean time that her journey takes is 30 minutes. In order to check this, Beth selects a random sample of 8 journeys. The times in minutes for these 8 journeys are as follows.\\
$\begin{array} { l l l l l l l l } 31.9 & 28.5 & 35.9 & 31.0 & 30.2 & 34.9 & 28.9 & 31.3 \end{array}$
\begin{enumerate}[label=(\alph*)]
\item What assumption does Beth need to make in order to construct a confidence interval for the mean journey time based on the $t$ distribution?
\item In this question you must show detailed reasoning.
Given that the assumption in part (a) is valid, determine a 95\% confidence interval for the mean journey time.
\item Explain whether the confidence interval suggests that Beth may be correct in the belief that her mean journey time is 30 minutes.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics B AS 2022 Q1 [10]}}