| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2020 |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | Calculate Type I error probability |
| Difficulty | Standard +0.3 This is a straightforward application of hypothesis testing with binomial distributions. Part (a) requires basic understanding of one-tailed tests, part (b) involves standard critical region calculation using cumulative binomial probabilities, and part (c) is a simple comparison with the critical region. All steps are routine textbook procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
At a certain hospital it was found that the probability that a patient did not arrive for an appointment was 0.1. The hospital's business model assumed that this probability will be reduced. They wish to test whether this probability is now less than 0.1.
A random sample of 50 appointments is selected and the number of patients that did not arrive is noted. This figure is used as a test statistic at the 5\% significance level.
\begin{enumerate}[label=(\alph*)]
\item Explain why this test is a one-tailed test and state suitable null and alternative hypotheses. [2]
\item Use a binomial distribution to find the critical region and find the probability of a Type I error. [5]
\item In fact 3 patients out of the 50 did not arrive.
State the conclusion of the test, explaining your answer. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2020 Q6 [9]}}