| Exam Board | OCR |
|---|---|
| Module | FS1 AS (Further Statistics 1 AS) |
| Year | 2017 |
| Session | Specimen |
| Marks | 4 |
| Topic | Chi-squared goodness of fit |
| Type | Chi-squared with algebraic frequencies |
| Difficulty | Standard +0.3 This is a straightforward chi-squared test calculation requiring students to set up the test statistic formula with expected frequencies (each N since probabilities are 1/3), substitute the given observed frequencies, set equal to 0.3, and solve a simple quadratic equation. It's slightly easier than average as it's a direct application of a standard formula with clear algebraic steps. |
| Spec | 5.06b Fit prescribed distribution: chi-squared test5.06c Fit other distributions: discrete and continuous |
| \(x\) | 0 | 1 | 2 |
| Observed frequency | \(N - 1\) | \(N - 1\) | \(N + 2\) |
The 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{center}
\begin{tabular}{|c|c|c|c|}
\hline
$x$ & 0 & 1 & 2 \\
\hline
Observed frequency & $N - 1$ & $N - 1$ & $N + 2$ \\
\hline
\end{tabular}
\end{center}
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 FS1 AS 2017 Q7 [4]}}