| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics B AS (Further Statistics B AS) |
| Year | 2021 |
| Session | November |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Z-tests (known variance) |
| Type | One-tail z-test (upper tail) |
| Difficulty | Standard +0.3 This is a straightforward one-sample z-test with clearly stated hypotheses and given variance. Part (a) requires standard hypothesis test procedure (calculate sample mean, test statistic, compare to critical value), parts (b) and (d) test understanding of causation vs correlation and Type I errors respectively, and part (c) requires naming the t-test. All components are routine bookwork for Further Statistics with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (a) | DR |
| Answer | Marks |
|---|---|
| than 8.3 kg | B1 |
| Answer | Marks |
|---|---|
| [7] | 1.1 |
| Answer | Marks |
|---|---|
| 3.5a | Hypotheses in words only must |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (b) | No because although there is sufficient evidence to |
| Answer | Marks |
|---|---|
| the cause. | E1 |
| Answer | Marks |
|---|---|
| [2] | 3.2a |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (c) | t test |
| [1] | 1.1 | Allow ‘Wilcoxon signed rank |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (d) | Because if the null hypothesis is true, by random |
| Answer | Marks |
|---|---|
| result in rejection of the null hypothesis | E1 |
| Answer | Marks |
|---|---|
| [2] | 2.2a |
Question 3:
3 | (a) | DR
Sample mean weight in other river = 9.31
H : μ = 8.3 H : μ > 8.3
0 1
Where μ is the population weight of male otters in
the other river
Test statistic is
9.31−8.3
= 1.683
1.8/√9
Critical value (1-tailed) at 5% level is 1.645
1.683 > 1.645 so significant ( reject H )
0
Sufficient evidence to suggest that the average
weight of male otters in the other river is greater
than 8.3 kg | B1
B1
B1
M1
A1
B1
B1
[7] | 1.1
1.1a
2.5
3.3
1.1
1.1
3.5a | Hypotheses in words only must
include “population”.
For definition in context.
No FT if not 1.645
AG
3 | (b) | No because although there is sufficient evidence to
suggest that the average weight of male otters in
the other river is greater than 8.3 kg, there is
nothing to suggest that better availability of food is
the cause. | E1
E1
[2] | 3.2a
3.2b
3 | (c) | t test | 1
[1] | 1.1 | Allow ‘Wilcoxon signed rank
test’
3 | (d) | Because if the null hypothesis is true, by random
variation if the test were to be repeated many
times, an average of one in twenty tests would
result in rejection of the null hypothesis | E1
E1
[2] | 2.2a
1.23 The weights in kg of male otters in a large river system are known to be Normally distributed with mean 8.3 and standard deviation 1.8. A researcher believes that weights of male otters in another river are higher because of what he suspects is better availability of food. The researcher records the weights of a random sample of 9 male otters in this other river. The sum of these 9 weights is 83.79 kg .
\begin{enumerate}[label=(\alph*)]
\item In this question you must show detailed reasoning.
You should assume that:
\begin{itemize}
\item the weights of otters in the other river are Normally distributed,
\item the standard deviation of the weights of otters in the other river is also 1.8 kg .
\end{itemize}
Show that a test at the $5 \%$ significance level provides sufficient evidence to conclude that the mean weight of male otters in the other river is greater than 8.3 kg .
\item Explain whether the result of the test suggests that the weights are higher due to better availability of food.
\item If the standard deviation of the weights of otters in the other river could not be assumed to be 1.8 kg , name an alternative test that the researcher could carry out to investigate otter weights.
\item Explain why, even if a test at the $5 \%$ significance level results in the rejection of the null hypothesis, you cannot be sure that the alternative hypothesis is true.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics B AS 2021 Q3 [12]}}