Statistical inference
Draw conclusions from a set of data 
Put a probability on whether a conclusion is correct ‘beyond reasonable doubt’ 
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 
Twotailed or onetailed
The alternative hypothesis may be classified as twotailed or onetailed 
Twotailed test 
 
is a twosided alternative 
 
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 
 
the alternative hypothesis is written: H1: µ =/= µo 
Onetailed test 
 
onesided alternative 
 
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 
 
E.g. the alternative hypothesis is written as: H1: µ > µo 


Decisionmaking process steps
1. 
Collecting the data 
2. 
Summarising the data 
3. 
Setting up a hypothesis (i.e. a claim or theory), which is to be tested 
4. 
Calculating the probability of obtaining a sample such as the one we have if the hypothesis is true 
5. 
Either accepting or rejecting the hypothesis 
Significance level
After the appropriate hypotheses have been formulated, we must decide upon the significance level (or α level) of the test 
most common significance level used is 0.05, commonly written as α = 0.05 
A 5% significance level says in effect that an event has occurred that occurs less than 5% of the time is considered unusual 
Onesample ztest
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 
Construct a test statistic according to a particular formula 
Information required in calculation 
 
the size (n) of the sample 
 
the mean of the sample 
 
the standard deviation (s) of the sample 
Other information of interest might include: 
 
Does the population have a normal distribution? 
 
Is the population’s standard deviation known? 
 
Is the sample size (n) large? (25+) 
There are different cases for the onesample ztest statistic 
Case I 
the population has a normal distribution and 
the population standard deviation, s, is known 
Case II 
the population has any distribution 
the sample size, n, is large (i.e. at least 25), and 
the value of population standard deviation is known 
In both these cases we can use a ztest statistic formula (a) 
Case III 
the population has any distribution 
the sample size, n, is large (i.e. at least 25), and 
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) 
In this case we can use a ztest statistic formula (b) 


Set up your Hypothesis
Null Hypothesis 
Part of formulation of an hypothesis 
Statement that nothing unusual has occurred 
The notation is Ho 
Alternative hypothesis 
States that something unusual has occurred 
The notation is H1 or HA 
Together they may be written in the form: Ho: (statement) v. H1(alternative statement) 
Conclusion errors
Two possible errors in making a conclusion about a null hypothesis 
Type I errors occur when you reject H0 (i.e. conclude that it is false) when H0 is really true. 
Type II errors occur when you accept H0 (i.e. conclude that it is true) when H0 is really false. 
ztest statistic formula (a)
ztest statistic formula (b)

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