Language of hypothesis testingAQA A-Level Maths: Mind map

Exam questions on Language of hypothesis testing

1. A seed company claims that 60% of its seeds germinate. A gardener suspects that the true percentage is lower. She plants 20 seeds and records the number $X$ that germinate. She will test her suspicion at the 5% significance level, assuming that $X\sim B(20,p)$, where $p$ is the probability that a seed germinates. For reference, $P(X\le7)=0.0210$ and $P(X\le8)=0.0565$ when $p=0.6$.
   State the critical value of the test and write down the acceptance region.2 marks
2. A spinner has four equal-looking sections, one of which is red. The manufacturer says that the probability of the spinner landing on red is $0.25$. A teacher thinks the spinner may be biased, in either direction. She spins it 20 times and records the number $Y$ of reds, using $Y\sim B(20,p)$ and a 10% significance level. When $p=0.25$: $P(Y\le1)=0.0243$, $P(Y\le2)=0.0913$, $P(Y\ge8)=0.1018$ and $P(Y\ge9)=0.0409$.
   The teacher says: "A 10% significance level means there is a 10% chance that the spinner is biased." Explain why this is incorrect.2 marks
3. A café owner believes that 30% of customers order a cold drink. She runs an advert that is intended to increase this proportion. Afterwards she picks 15 customers at random and finds that 9 of them order a cold drink. Let $X$ be the number of cold drinks ordered by 15 customers, and test at the 5% significance level whether the proportion has increased.
   Write down the null and alternative hypotheses, and state the distribution of $X$ if the null hypothesis is true.3 marks