What is the alternative hypothesis?

What you accept if there is sufficient evidence against H0, such as H1:p<0.6 or H1:p\ne0.6.

When is a test 1-tail?

When H1 has a direction, p<p0 or pp0.

When is a test 2-tail?

When H1 says only that the parameter has changed: H1:p\ne p0.

What is a test statistic?

The value from the sample used to decide, for a binomial test the number of successes X.

What is the significance level?

The probability of rejecting H0 when H0 is true.

What is the critical region?

The values of the test statistic that lead to rejecting H0.

What is the critical value?

The boundary of the critical region.

What is the acceptance region?

The values of the test statistic for which H0 is not rejected.

The probability, assuming H0 is true, of a result at least as extreme as the one observed.

Decision rule using the p-value?

Reject H0 if the p-value \le the significance level.

What is the actual significance level?

The probability of the critical region when H0 is true; it is often less than the stated level for discrete data.

Language of hypothesis testingAQA A-Level Maths: Flashcards

Card 1 of 140 of 14 known

Question

What is the null hypothesis?

Tap or press Space to reveal

Tap card or press Space to flip

See all 14 cards

What is the null hypothesis?: The hypothesis assumed true when carrying out the test; it gives a single value, such as $H_0:p=0.6$ .
What is the alternative hypothesis?: What you accept if there is sufficient evidence against $H_0$ , such as $H_1:p<0.6$ or $H_1:p\ne0.6$ .
When is a test 1-tail?: When $H_1$ has a direction, $p<p_0$ or $p>p_0$ .
When is a test 2-tail?: When $H_1$ says only that the parameter has changed: $H_1:p\ne p_0$ .
What is a test statistic?: The value from the sample used to decide, for a binomial test the number of successes $X$ .
What is the significance level?: The probability of rejecting $H_0$ when $H_0$ is true.
What is the critical region?: The values of the test statistic that lead to rejecting $H_0$ .
What is the critical value?: The boundary of the critical region.
What is the acceptance region?: The values of the test statistic for which $H_0$ is not rejected.
What is a $p$ -value?: The probability, assuming $H_0$ is true, of a result at least as extreme as the one observed.
Decision rule using the $p$ -value?: Reject $H_0$ if the $p$ -value $\le$ the significance level.
How do you split 5% in a 2-tail test?: At most $2.5\%$ in each tail.
What is the actual significance level?: The probability of the critical region when $H_0$ is true; it is often less than the stated level for discrete data.
Upper tail probability $P(X\ge k)$ ?: $1-P(X\le k-1)$ .

Exam questions on Language of hypothesis testing

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
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
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

See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).