| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics B AS (Further Statistics B AS) |
| Year | 2019 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Central limit theorem |
| Type | Confidence interval interpretation |
| Difficulty | Standard +0.3 This question tests standard confidence interval interpretation and basic calculations. Parts (a)-(c) require understanding whether 250g falls within intervals and discussing statistical practice—routine conceptual knowledge. Part (d) involves straightforward algebraic manipulation to find variance from interval width. Part (e) asks for a textbook definition. While it's Further Maths content, these are foundational statistical concepts with no novel problem-solving required, making it slightly easier than average A-level difficulty. |
| Spec | 5.05d Confidence intervals: using normal distribution |
| Sample Mean | 248.92 |
| Standard Error | 0.61506 |
| Sample Size | 40 |
| Confidence Level | 0.95 |
| Interval | \(248.92 \pm 1.2055\) |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (a) | Confidence interval does not suggest that the |
| Answer | Marks |
|---|---|
| 250 | B1 |
| Answer | Marks |
|---|---|
| [2] | Max B1B0 if no element of |
| Answer | Marks |
|---|---|
| (b) | Confidence interval is given by |
| Answer | Marks |
|---|---|
| manager is correct | B1 |
| Answer | Marks |
|---|---|
| [3] | For 1.645 |
| (c) | No, it is not appropriate as the size of a confidence |
| Answer | Marks |
|---|---|
| adjusted to provide the conclusion that it desired. | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| [2] | Must have some justification | Allow E1E0 BOD if ‘No’ and |
| Answer | Marks |
|---|---|
| (d) | s2 |
| Answer | Marks |
|---|---|
| Variance s2 = 9.397 | M1 |
| Answer | Marks |
|---|---|
| [2] | Must use 1.96 |
| Answer | Marks |
|---|---|
| (e) | In repeated sampling, 95% of confidence intervals |
| Answer | Marks |
|---|---|
| population mean. | E1 |
Question 6:
6 | (a) | Confidence interval does not suggest that the
mean weight is different from 250 g because the
upper bound is 250.1255 so the interval contains
250 | B1
B1
[2] | Max B1B0 if no element of
doubt. Max B1B0 if upper
bound not stated.
(b) | Confidence interval is given by
248.92 1.645 0.61506
247.91 < μ < 249.93 or 248.92 1.01 so the
manager is correct | B1
M1
A1
[3] | For 1.645
(c) | No, it is not appropriate as the size of a confidence
interval should be decided before the interval is
calculated because otherwise the level can be
adjusted to provide the conclusion that it desired. | E1
E1
[2] | Must have some justification | Allow E1E0 BOD if ‘No’ and
there is a rather unclear
reason or if a larger sample is
suggested
(d) | s2
Width of interval = 21.96 = 1.9
40
Variance s2 = 9.397 | M1
A1
[2] | Must use 1.96
NB Sample sd = 3.065 which
gets M1A0
(e) | In repeated sampling, 95% of confidence intervals
constructed in this way will contain the true
population mean. | E1
E1
[2]
PPMMTT
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© OCR 20196 The label on a pack of strawberries in a large batch states that it holds 250 g of strawberries. A random sample of 40 packs from the batch is selected and software is used to produce a $95 \%$ confidence interval for the mean weight of strawberries per pack. An extract from the software output is shown in Fig. 6.
\begin{table}[h]
\begin{center}
\begin{tabular}{ | l l | }
\hline
Sample Mean & 248.92 \\
Standard Error & 0.61506 \\
Sample Size & 40 \\
Confidence Level & 0.95 \\
Interval & $248.92 \pm 1.2055$ \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 6}
\end{center}
\end{table}
\begin{enumerate}[label=(\alph*)]
\item Explain whether the confidence interval suggests that the mean weight of strawberries per pack in the batch is different from 250 g .
\item A manager looking at the data says that the conclusion would have been different if a $90 \%$ confidence interval had been used.\\
Determine whether the manager is correct.
\item Explain briefly whether or not it is appropriate for the manager to vary the confidence level before coming to any conclusions.\\[0pt]
\item On another occasion, using the same sample size, a 95\% confidence interval for the mean weight of strawberries per pack is [248.05, 249.95].\\
Find the sample variance in this case.
\item Explain the meaning of a 95\% confidence interval.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics B AS 2019 Q6 [11]}}