| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2017 |
| Session | March |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Z-tests (known variance) |
| Type | Two-tail z-test |
| Difficulty | Easy -1.2 This is a straightforward hypothesis testing question requiring only recall of standard definitions and procedures. Part (i) asks for the alternative hypothesis (simply H₁: μ ≠ 6.4), part (ii) requires comparing z = 2.43 to critical value 2.576 at 1% level (routine lookup), and part (iii) asks for a textbook explanation of when to use one-tail vs two-tail tests. No calculations, problem-solving, or novel insight required—pure recall of standard S2 content. |
| Spec | 2.05a Hypothesis testing language: null, alternative, p-value, significance2.05c Significance levels: one-tail and two-tail5.05c Hypothesis test: normal distribution for population mean |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((H_1): \mu \neq 6.4\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Compare \(2.43\) with a \(z\)-value, \(z = 2.576\) AND | M1 | oe valid comparison |
| No evidence that \(\mu\) is not \(6.4\) or do not reject \(\mu = 6.4\) | A1 | Allow "Accept \(\mu = 6.4\)". Must mention \(\mu\), not just "\(H_0\)" or "\(H_1\)" |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Testing for an increase in \(\mu\), or for a decrease in \(\mu\), rather than a change | B1 | Any equiv statement |
## Question 2(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(H_1): \mu \neq 6.4$ | B1 | |
## Question 2(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Compare $2.43$ with a $z$-value, $z = 2.576$ AND | M1 | oe valid comparison |
| No evidence that $\mu$ is not $6.4$ or do not reject $\mu = 6.4$ | A1 | Allow "Accept $\mu = 6.4$". Must mention $\mu$, not just "$H_0$" or "$H_1$" |
## Question 2(iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Testing for an increase in $\mu$, or for a decrease in $\mu$, rather than a change | B1 | Any equiv statement |
---2 Karim has noted the lifespans, in weeks, of a large random sample of certain insects. He carries out a test, at the $1 \%$ significance level, for the population mean, $\mu$. Karim's null hypothesis is $\mu = 6.4$.\\
(i) Given that Karim's test is two-tail, state the alternative hypothesis.\\
Karim finds that the value of the test statistic is $z = 2.43$.\\
(ii) Explain what conclusion he should draw.\\
(iii) Explain briefly when a one-tail test is appropriate, rather than a two-tail test.\\
\hfill \mbox{\textit{CAIE S2 2017 Q2 [4]}}