Summary sheet: Statistical hypothesis testing
O1 Understand and apply the language of statistical hypothesis testing, developed through a
binomial model: null hypothesis, alternative hypothesis, significance level, test statistic,
1-tail test, 2-tail test, critical value, critical region, acceptance region, p-value
O2 Conduct a statistical hypothesis test for the proportion in the binomial distribution and
interpret the results in context
Understand that a sample is being used to make an inference about the population and
appreciate that the significance level is the probability of incorrectly rejecting the null
hypothesis
Hypothesis testing
A hypothesis test uses statistical techniques to test a particular claim (the hypothesis). In a hypothesis
test, a sample from the population is used to see if the result from that sample is consistent with the
claim.
Hypothesis testing using the binomial distribution
In a hypothesis test using the binomial distribution B(n, p), you are testing whether the population
proportion (p) takes a particular value. For example, you might want to decide whether a six-sided
spinner is biased, and you might test this by spinning it 20 times and seeing how many sixes come up.
1. Setting up the hypotheses
The first step is to state the hypotheses for the test.
• The null hypothesis, denoted as H0, is that p takes a particular value. This would be the value
that you might expect (e.g. if you are counting the number of sixes that come up when you spin a
fair six-sided spinner 50 times, you would expect p to be 16 ).
You write: H0: p = 16 .
• The alternative hypothesis, denoted as H1, takes one of three forms, depending on what you are
testing.
o If you think the spinner is biased so that it is more likely to show a six, the alternative
hypothesis is H1: p 16 .
o If you think the spinner is biased so that it is less likely to show a six, the alternative
hypothesis is H1: p 16 .
o If you think the spinner is biased but you don’t know which way, the alternative
hypothesis is H1: p 16 .
If the alternative hypothesis involves < or >, the test is a one-tailed test. You are testing to see if there
has been a change, or something unusual, in a particular direction.
If the alternative hypothesis involves , the test is a two-tailed test. You are testing to see if there has
been a change, or something unusual, but it could be in either direction.
2. The significance level
The significance level needs to be set before carrying out the test. Often a significance level of 5% is
used, but other significance levels could be used. The significance level is the probability of rejecting the
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O1 Understand and apply the language of statistical hypothesis testing, developed through a
binomial model: null hypothesis, alternative hypothesis, significance level, test statistic,
1-tail test, 2-tail test, critical value, critical region, acceptance region, p-value
O2 Conduct a statistical hypothesis test for the proportion in the binomial distribution and
interpret the results in context
Understand that a sample is being used to make an inference about the population and
appreciate that the significance level is the probability of incorrectly rejecting the null
hypothesis
Hypothesis testing
A hypothesis test uses statistical techniques to test a particular claim (the hypothesis). In a hypothesis
test, a sample from the population is used to see if the result from that sample is consistent with the
claim.
Hypothesis testing using the binomial distribution
In a hypothesis test using the binomial distribution B(n, p), you are testing whether the population
proportion (p) takes a particular value. For example, you might want to decide whether a six-sided
spinner is biased, and you might test this by spinning it 20 times and seeing how many sixes come up.
1. Setting up the hypotheses
The first step is to state the hypotheses for the test.
• The null hypothesis, denoted as H0, is that p takes a particular value. This would be the value
that you might expect (e.g. if you are counting the number of sixes that come up when you spin a
fair six-sided spinner 50 times, you would expect p to be 16 ).
You write: H0: p = 16 .
• The alternative hypothesis, denoted as H1, takes one of three forms, depending on what you are
testing.
o If you think the spinner is biased so that it is more likely to show a six, the alternative
hypothesis is H1: p 16 .
o If you think the spinner is biased so that it is less likely to show a six, the alternative
hypothesis is H1: p 16 .
o If you think the spinner is biased but you don’t know which way, the alternative
hypothesis is H1: p 16 .
If the alternative hypothesis involves < or >, the test is a one-tailed test. You are testing to see if there
has been a change, or something unusual, in a particular direction.
If the alternative hypothesis involves , the test is a two-tailed test. You are testing to see if there has
been a change, or something unusual, but it could be in either direction.
2. The significance level
The significance level needs to be set before carrying out the test. Often a significance level of 5% is
used, but other significance levels could be used. The significance level is the probability of rejecting the
1 of 3 12/05/21 © MEI
integralmaths.org
