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Draw conclusions from a set of data
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Put a probability on whether a conclusion is correct ‘beyond reasonable doubt’
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The major question to answer is whether a difference between samples, or between a sample and a population, has occurred simply as a result of natural variation or because of a real difference between the two
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The alternative hypothesis may be classified as two-tailed or one-tailed
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Two-tailed test
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is a two-sided alternative
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we do the test with no preconceived notion that the true value of μ is either above or below the hypothesised value of μ 0
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the alternative hypothesis is written: H1: µ =/= µo
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One-tailed test
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one-sided alternative
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do the test with a strong conviction that, if H0 is not true, it is clear that m is either grater than µ0 or less than µ0
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E.g. the alternative hypothesis is written as: H1: µ > µo
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1.
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Collecting the data
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2.
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Summarising the data
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3.
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Setting up a hypothesis (i.e. a claim or theory), which is to be tested
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4.
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Calculating the probability of obtaining a sample such as the one we have if the hypothesis is true
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5.
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Either accepting or rejecting the hypothesis
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After the appropriate hypotheses have been formulated, we must decide upon the significance level (or α -level) of the test
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most common significance level used is 0.05, commonly written as α = 0.05
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A 5% significance level says in effect that an event has occurred that occurs less than 5% of the time is considered unusual
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Deals with the case of a single sample being chosen from a population and the question of whether that particular sample might be consistent with the rest of the population
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Construct a test statistic according to a particular formula
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Information required in calculation
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the size (n) of the sample
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the mean of the sample
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the standard deviation (s) of the sample
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Other information of interest might include:
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Does the population have a normal distribution?
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Is the population’s standard deviation known?
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Is the sample size (n) large? (25+)
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There are different cases for the one-sample z-test statistic
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Case I
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the population has a normal distribution and
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the population standard deviation, s, is known
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Case II
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the population has any distribution
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the sample size, n, is large (i.e. at least 25), and
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the value of population standard deviation is known
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In both these cases we can use a z-test statistic formula (a)
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Case III
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the population has any distribution
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the sample size, n, is large (i.e. at least 25), and
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the value of population standard devation is unknown (however, since n is large, the value of population standard devation is approximated by the sample standard deviation, s)
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In this case we can use a z-test statistic formula (b)
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Null Hypothesis
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Part of formulation of an hypothesis
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Statement that nothing unusual has occurred
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The notation is Ho
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Alternative hypothesis
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States that something unusual has occurred
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The notation is H1 or HA
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Together they may be written in the form: Ho: (statement) v. H1(alternative statement)
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Two possible errors in making a conclusion about a null hypothesis
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Type I errors occur when you reject H0 (i.e. conclude that it is false) when H0 is really true.
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Type II errors occur when you accept H0 (i.e. conclude that it is true) when H0 is really false.
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