| Exam Board | OCR |
|---|---|
| Module | Further Statistics AS (Further Statistics AS) |
| Session | Specimen |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared goodness of fit |
| Type | Chi-squared with algebraic frequencies |
| Difficulty | Standard +0.3 This is a straightforward chi-squared calculation requiring students to set up the expected frequencies (each N since probabilities are 1/3), apply the chi-squared formula, and solve a simple quadratic equation. It's slightly easier than average as it's a direct application of a standard formula with algebraic manipulation, requiring no conceptual insight beyond knowing the chi-squared test statistic formula. |
| Spec | 5.06b Fit prescribed distribution: chi-squared test |
| \(x\) | 0 | 1 | 2 |
| Observed frequency | \(N - 1\) | \(N - 1\) | \(N + 2\) |
| Answer | Marks |
|---|---|
| 7 | (O(cid:16)E)2 1 1 22 |
| Answer | Marks |
|---|---|
| N | M1 |
| Answer | Marks |
|---|---|
| [4] | 3.1a |
| Answer | Marks |
|---|---|
| 1.1 | Correct formula used |
Question 7:
7 | (O(cid:16)E)2 1 1 22
(cid:166) (cid:32) (cid:14) (cid:14)
E N N N
6
(cid:32)0.3 so N = 20
N | M1
A1
M1
A1
[4] | 3.1a
1.1
1.1
1.1 | Correct formula used
Correct (O – E)2 values
Obtain 20 only
7
n
e
m
i
c
e
p
SThe discrete random variable $X$ is equally likely to take values 0, 1 and 2. $3N$ observations of $X$ are obtained, and the observed frequencies corresponding to $X = 0$, $X = 1$ and $X = 2$ are given in the following table.
\begin{tabular}{|c|c|c|c|}
\hline
$x$ & 0 & 1 & 2 \\
\hline
Observed frequency & $N - 1$ & $N - 1$ & $N + 2$ \\
\hline
\end{tabular}
The test statistic for a chi-squared goodness of fit test for the data is 0.3. Find the value of $N$. [4]
\hfill \mbox{\textit{OCR Further Statistics AS Q7 [4]}}