What is the alternative hypothesis?

What we accept if H0 is rejected: pp0, p<p0 or p\ne p0.

In terms of what are hypotheses written?

The population parameter p, not the sample statistic X.

What is the test statistic?

The value calculated from the sample, such as the number of successes X.

What is the significance level?

The probability of incorrectly rejecting H0 when it is true.

One-tailed or two-tailed: H1:p\ne0.4?

Two-tailed; the significance level is split equally between the tails.

What is the critical region?

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

What is the acceptance region?

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

What is a critical value?

The boundary of the critical region.

What is the actual significance level?

The probability of the whole critical region when H0 is true.

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

When is H0 rejected using a p-value?

When the p-value is less than or equal to the significance level (halved in a two-tailed test).

How do you use np0 in a two-tailed test?

To decide which tail the observation is in: below np0 is the lower tail, above is the upper tail.

Language of hypothesis testingEdexcel A-Level Maths: Flashcards

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What is the null hypothesis?

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What is the null hypothesis?: The assumption being tested, $H_0:p=p_0$ , taken to be true unless evidence is strong against it.
What is the alternative hypothesis?: What we accept if $H_0$ is rejected: $p>p_0$ , $p<p_0$ or $p\ne p_0$ .
In terms of what are hypotheses written?: The population parameter $p$ , not the sample statistic $X$ .
What is the test statistic?: The value calculated from the sample, such as the number of successes $X$ .
What is the significance level?: The probability of incorrectly rejecting $H_0$ when it is true.
One-tailed or two-tailed: $H_1:p\ne0.4$ ?: Two-tailed; the significance level is split equally between the tails.
Two-tailed test at 10%: how much in each tail?: 5% in each tail.
What is the critical region?: The values of the test statistic that lead to rejecting $H_0$ .
What is the acceptance region?: The values of the test statistic for which $H_0$ is not rejected.
What is a critical value?: The boundary of the critical region.
What is the actual significance level?: The probability of the whole critical region when $H_0$ is true.
Define the $p$ -value.: The probability of a result at least as extreme as the one observed, assuming $H_0$ is true.
When is $H_0$ rejected using a $p$ -value?: When the $p$ -value is less than or equal to the significance level (halved in a two-tailed test).
How do you use $np_0$ in a two-tailed test?: To decide which tail the observation is in: below $np_0$ is the lower tail, above is the upper tail.

Exam questions on Language of hypothesis testing

A coin is suspected of being biased towards heads. Let $p$ be the probability that the coin lands heads. The coin is tossed 20 times and $X$ is the number of heads. A hypothesis test is carried out at the 5% significance level.
The critical region for this test is $X\ge15$ . Find the actual probability of rejecting $H_0$ when it is true.2 marks
A die is thought to be biased with respect to sixes. Let $p$ be the probability that the die lands on six. The die is rolled 30 times and $X$ is the number of sixes. The test of $H_0:p=\frac16$ against $H_1:p\ne\frac16$ is carried out at the 10% significance level.
Find the critical region for the lower tail of this test.2 marks
A manufacturer claims that 20% of its chocolate eggs contain a toy. A child believes that the proportion is greater than 20%. In a random sample of 25 eggs, 9 contain a toy. Let $p$ be the proportion of all the manufacturer's eggs that contain a toy, and let $X$ be the number of eggs in a sample of 25 that contain a toy.
State the null and alternative hypotheses, and state the distribution of $X$ if the null hypothesis is true.3 marks

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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).