| Exam Board | OCR |
|---|---|
| Module | FS1 AS (Further Statistics 1 AS) |
| Year | 2021 |
| Session | June |
| Marks | 9 |
| Topic | Chi-squared goodness of fit |
| Type | Chi-squared with algebraic frequencies |
| Difficulty | Challenging +1.2 This is a chi-squared goodness-of-fit test requiring students to set up hypotheses, calculate expected frequencies for U(20), form the test statistic as a function of y, and solve an inequality involving the critical value. While it involves multiple steps and algebraic manipulation of the chi-squared statistic, the underlying concepts are standard FS1 material with no novel insights required—just systematic application of the test procedure. |
| Spec | 5.06c Fit other distributions: discrete and continuous |
| Range | \(1 \leq x \leq 8\) | \(9 \leq x \leq 12\) | \(13 \leq x \leq 20\) |
| Observed frequency | 12 | \(y\) | \(28 - y\) |
The table shows the results of a random sample drawn from a population which is thought to have the distribution $U(20)$.
\begin{tabular}{|c|c|c|c|}
\hline
Range & $1 \leq x \leq 8$ & $9 \leq x \leq 12$ & $13 \leq x \leq 20$ \\
\hline
Observed frequency & 12 & $y$ & $28 - y$ \\
\hline
\end{tabular}
Find the range of values of $y$ for which the data are not consistent with the distribution at the $5\%$ significance level. [9]
\hfill \mbox{\textit{OCR FS1 AS 2021 Q4 [9]}}