Suppose we had population distributions that looked like these:
Say the mean was equal to 40, if we took a random sample from this population of a certain size n… over and over again and calculated the mean each time……
We could make a distribution of nothing but those means. This would be a sampling distribution of means.
Central Limit Theorem If samples are large, then the sampling distribution created by those samples will have a mean equal to the population mean and a standard deviation equal to the standard error.
Type I and Type TT errors –Type I ： reject the correct original Hypothesis ， called Producer's Risk –Type II ： accept the wrong original Hypothesis ， called Consumer’s Risk Population condition conclu sion H o true H a true AcceptH 0 correct type TT error conclusion RejectH 0 Type I error correct conclusion
We denote the probabilities of making the two errors as follows: α——the probability of making a Type I error β——the probability of making a Type TT error In practice ， the person conducting the hypothesis test specifies the maximum allowable probability of making a Type I error ， called the level of significance for the test 。 Common choices for the level of significance are α=0.05 orα= 0.01 。 Type I and Type TT errors
Steps of Hypothesis Testing 1.Determine the null and alternative hypotheses. 2.Specify the level of significance . 3.Collect the sample data and calculate the test statistic. Using the p -Value 4.Use the value of the test statistic to compute the p - value. 5.Reject H 0 if p -value < .
Steps of Hypothesis Testing Using the Critical Value 4.Use to determine the critical value for the test statistic and the rejection rule. 5.Use the value of the test statistic and the rejection rule to determine whether to reject H 0.