Standard +0.3 This is a straightforward application of binomial hypothesis testing requiring students to find critical values from tables at a non-standard significance level (4%). While it involves some table work and understanding of one-tailed tests, it's a standard procedure with no conceptual surprises—slightly easier than average since it's purely mechanical once the setup is recognized.
9 Briony suspects that a particular 6-sided dice is biased in favour of 2. She plans to throw the dice 35 times and note the number of times that it shows a 2 . She will then carry out a test at the \(4 \%\) significance level. Find the rejection region for the test.
\(H_1: p>\frac{1}{6}\) where \(p=P(2\) on one throw\()\)
B1
AO 2.5
\(B(35,\frac{1}{6})\)
M1
AO 3.3
\(P(X\geq 10)=1-P(X\leq 9)\) or \(P(X\geq 11)=1-P(X\leq 10)\)
M1
AO 1.1a
\(P(X\geq 10)=0.055\)
A1
AO 2.1
\(P(X\geq 11)=0.023\)
A1
AO 3.4
(0.04 lies between these hence) rejection region is \(X\geq 11\), Allow \(a\geq 11\)
A1 [7]
AO 2.2a
Special case using N~Bin; Method A: \(H_0: \mu=\frac{35}{6}\)
B1
AO 1.1
## Question 9:
$H_0: p=\frac{1}{6}$ | **B1** | AO 1.1 |
$H_1: p>\frac{1}{6}$ where $p=P(2$ on one throw$)$ | **B1** | AO 2.5 | **B1B0** one error eg undefined $p$ or two-tail
$B(35,\frac{1}{6})$ | **M1** | AO 3.3 | stated or implied unless clearly using N()
$P(X\geq 10)=1-P(X\leq 9)$ or $P(X\geq 11)=1-P(X\leq 10)$ | **M1** | AO 1.1a | $\geq 1$ of these probabilities stated; or $P(X\leq 9)$, $P(X\leq 10)$
$P(X\geq 10)=0.055$ | **A1** | AO 2.1 | BC; $P(X\leq 9)=0.945$
$P(X\geq 11)=0.023$ | **A1** | AO 3.4 | BC; $P(X\leq 10)=0.977$ (0.96 between these)
(0.04 lies between these hence) rejection region is $X\geq 11$, Allow $a\geq 11$ | **A1** [7] | AO 2.2a | dep $\geq$ one of above probs seen & correct; rej'n region is $X\geq 11$
Special case using N~Bin; Method A: $H_0: \mu=\frac{35}{6}$ | **B1** | AO 1.1 |
9 Briony suspects that a particular 6-sided dice is biased in favour of 2. She plans to throw the dice 35 times and note the number of times that it shows a 2 . She will then carry out a test at the $4 \%$ significance level. Find the rejection region for the test.
\hfill \mbox{\textit{OCR H240/02 2018 Q9 [7]}}