Moderate -0.5 This is a straightforward application of a binomial hypothesis test with clearly defined parameters (n=10, p=0.2 under H₀). Students must state hypotheses, calculate P(X≥4) using binomial tables, and compare to 5%. While it requires understanding of hypothesis testing framework, it's a standard textbook exercise with no conceptual surprises, making it slightly easier than average.
A student takes a multiple choice test. The test is made up of 10 questions each with 5 possible answers. The student gets 4 questions correct. Her teacher claims she was guessing the answers. Using a one tailed test, at the 5\% level of significance, test whether or not there is evidence to reject the teacher's claim.
State your hypotheses clearly.
[6]
OR \(P(X \leq 4) = 0.9672\) and \(P(X \geq 5) = 0.0328\); CR \(X \geq 5\)
A1
\(0.1209 > 0.05\). Insufficient evidence to reject \(H_0\) so teacher's claim is supported.
M1A1ft
Notes:
- B1 for both \(H_0\) and \(H_1\) correct. Must use \(p\) or \(\pi\) (pi).
- B1 for writing or using \(\text{Bin}(10,0.2)\).
- M1 for finding or writing \(1 - P(X \leq 3)\) or \(P(X \leq 4) = 0.9672\) or \(P(X \geq 5) = 0.0328\) or a correct critical region.
- A1 awrt 0.121 or CR \(X \geq 5\).
- M1 need \(p<0.5\) and: correct statement using their Probability and 0.05 if one tail test or correct statement using their Probability and 0.025 if two tail test (condone a comparison with 0.05 instead of 0.025 for a two tail test).
- Do not allow non-contextual conflicting statements eg "significant" and "accept \(H_0\)".
- A1 ft correct contextual statement followed through from "their prob".
- Either a comment on whether the teacher's claim was correct or on whether the student was guessing the answers.
- NB if a correct contextual statement only is given for their probability then award M1 A1.
- If \(p>0.5\): They may compare with 0.95 (one tail method) or 0.975 (two tail method). Probability is 0.8791.
[6 marks total]
$H_0: p = 0.2$; $H_1: p > 0.2$ | B1, B1 |
Under $H_0$, $X \sim \text{Bin}(10,0.2)$ | B1 |
$P(X \geq 4) = 1 - P(X \leq 3) = 1 - 0.8791 = 0.1209$ | M1 |
OR $P(X \leq 4) = 0.9672$ and $P(X \geq 5) = 0.0328$; CR $X \geq 5$ | A1 |
$0.1209 > 0.05$. Insufficient evidence to reject $H_0$ so teacher's claim is supported. | M1A1ft |
**Notes:**
- B1 for both $H_0$ and $H_1$ correct. Must use $p$ or $\pi$ (pi).
- B1 for writing or using $\text{Bin}(10,0.2)$.
- M1 for finding or writing $1 - P(X \leq 3)$ or $P(X \leq 4) = 0.9672$ or $P(X \geq 5) = 0.0328$ or a correct critical region.
- A1 awrt 0.121 or CR $X \geq 5$.
- M1 need $p<0.5$ and: correct statement using their Probability and 0.05 if one tail test or correct statement using their Probability and 0.025 if two tail test (condone a comparison with 0.05 instead of 0.025 for a two tail test).
- Do not allow non-contextual conflicting statements eg "significant" and "accept $H_0$".
- A1 ft correct contextual statement followed through from "their prob".
- Either a comment on whether the teacher's claim was correct or on whether the student was guessing the answers.
- NB if a correct contextual statement only is given for their probability then award M1 A1.
- If $p>0.5$: They may compare with 0.95 (one tail method) or 0.975 (two tail method). Probability is 0.8791.
**[6 marks total]**
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A student takes a multiple choice test. The test is made up of 10 questions each with 5 possible answers. The student gets 4 questions correct. Her teacher claims she was guessing the answers. Using a one tailed test, at the 5\% level of significance, test whether or not there is evidence to reject the teacher's claim.
State your hypotheses clearly.
[6]
\hfill \mbox{\textit{Edexcel S2 2011 Q2 [6]}}