Statistical inferenceDraw 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 onetailedThe 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 steps1.  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 levelAfter 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 ztestDeals 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 HypothesisNull 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 errorsTwo 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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