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inferential statistics 2 ways to state a statistical hypothesis first is the null hypothesis H0, this is the chance hypothesis says there is no significant relationship
although the null states the difference should be zero, this shouldn't be taken too literally, a certain amount of fluctuation is expected
question is, how big can the difference be and not be considered significant? to do this we use standard error
however pop std usually unknown so we use the std of the sample
second method of stating a hypothesis is called the alternate H1 says there is a significant difference
there are 6 steps in hypothesis testing 1) formulae the hypothesis, H0 or H1 2) specify the appropriate sample statistic and its sampling distribution 3) select a level of significance ( ")4) construct a decision rule 5) compute the value of the test statistic 6) make the decision specifying the sample statistic test statistics divided into 2 groups: parametric and nonparametric parametric tests are based on hypothesis concerning population parameters 1) assumed samples are drawn form normally distributed population 2) assumes homogeneity of variance, that is variances within the subsamples are assumed to homogeneous from subsample to subsample, if this is violated test is seriously compromised 3) assumed data is measured on continuous metric scale
computing test statistics
test statistics = computed statistic - hypothesized parameter standard error of the computed statistic
the key is the selection of the test distribution
significance of the difference between 0 and : when F is knownuse the z test
where 0 is calculated from the sample: is the hypothesized parameterF 0 is the standard error or the standard deviation of the sampling distributions of the means which is computed by F/n1/2
confidence limits how far from the population mean would the sample mean have to deviate to cause one not to accept H0
when the random sample size is large X can be assumed to be normally distributed confidence limits for : when F is knownquestion might arise, how far from the population mean would sample mean have to be to cause one not to accept H0 from knowledge of the normal distribution, regardless of where 0 is located relative to :, approximately 95% of the possible values of 0 that make up the distribution are within 2 std devs of the meanthe lower and upper limits for 0 are : -1.960 and : +1.960this is the confidence interval for :given the sample mean 0 and Z value, the lower and upper confidence limits may be computed by
where you can't be sure that population mean falls with the limits but you can 95% confident that it does |
