module 22 wrap up hypothesis test for population mean let's summarize in this hypothesis test for a population mean module we looked at the four steps of a hypothesis test as they relate to Claim about a a population mean step one determine the hypotheses the hypothesis or claims about the population mean new the no hypothesis is a is a hypothesis that the mean equals a specific value in this case mu not the alternative hypothesis is the competing claim that mu is less than greater than or not equal to mu here we have the alternative hypothesis and symbols these two where we claim that mu is less than mu or mu is greater than mu these are one tests when the alternative hypothesis is that mu is not equal to Mu not the test is a two test in the case of a matched pairs design the variable is the difference in two measurements and mu is the mean of the differences in the population step two collect the data since the hypothesis test is based on probability random selection or assignment is essential in data production additionally we need to check whether the t- model is a good fit for the sample and distribution of the sample means to use the t- model the variable must be normally distributed in the population or the sample size must be more than 30 in practice it is often impossible to verify that the variable is normally distributed in the population if this is the case and the sample size is not more than 30 researchers often use the t- model if the sample is not strongly skewed and does not have outliers step three assess the evidence if a t- model is appropriate determine the test statistic for the data sample mean in this case we have that t is equal to x - mu / s /un n use the test statistic together with the alternative hypothesis to determine the P value the P value is the probability of finding a random sample with a mean at least as Extreme as our sample mean assuming that the null hypothesis is true as in all hypothesis tests if the alternative hypothesis is greater than the P value is the area to the right of the test statistic if the alternative hypothesis is less than the P value is the area to the left of the test statistic if the alternative hypothesis is not equal to the P value is equal to double the tell area beyond the test statistic give the conclusion the logic of the hypothesis test is always the same to State a conclusion about the N hypothesis we compare the P value to the significance level Alpha if the P value is less than or equal to Alpha we reject the null we conclude there is significant evidence in favor of the alternative if p is greater than Alpha we failed to reject the null hypothesis we conclude the sample does not provide significant significant evidence in favor of the alternative we're at the conclusion and context of the research question our conclusion is usually a statement about the alternative hypothesis we accept the alternative or fail to reject the alternative and should indicate include the P value other hypothesis testing notes remember that the P value is the probability of seeing a sample M sample mean at least as Extreme as the one from the data if the N hypothesis is true the probability is about the random sample it is not a chance statement about the null or alternative hypothesis hypothesis tests are based on probability so there is always a chance that the data has led us to make an error if our test results in rejecting the no hypothesis that is actually true then this is called a type one error if our test results in failing to reject the no hypothesis that is actually false then it is called a type two error if rejecting a n hypothesis would be very expensive controversial or dang then we really want to avoid a type one error in this case we would set a strict significance level a small value of alpha such as 01 finally remember the phrase garbage and garbage out if the data collection methods are poor then the result of a hypothesis test are meaningless