Transcript T test
Hypothesis Testing Using T test Statistic Hypothesis Statement H1: College students sleep less than most folks H0: College students sleep the same or more than most folks The statistic you need to decide whether to reject or fail to reject the Null Hypothesis is the one-sample t test. This statistic compares the sample mean to the population mean and gets an estimate of the probability that the sample mean is different by chance. Example The average sleep time for the population is found to be 8 hours a day We think college students sleep a different amount, maybe more - maybe less. We survey 10 students to see how much they sleep. Let us assume that the average sleep time is less. The question is: Did you happen to pick a group of light sleepers by chance? Or do college kids really sleep less? Findings Population mean = 8 hours Data collected from 10 students Hours sleep per day : 3,4,5,5,5,5,6,6,6,7 Mean = 5.2 hours Std Dev = 1.1353 Std Error of the mean = 0.3590 Df = 9 Computer Generated Statistics Here's the output from a computer package: SE = SD / √N Reject / Fail to Reject? Does Your Group Come From a Different Population Than the One Specified? Population mean = 8 Sample mean = 5.2 2 Possibilities: Your sample comes from a different population - reject the Null Hypothesis. The group comes from the same population and the mean varies by chance. You just happened to pick a sample group with a mean that misrepresents the population it came from. The group isn't really different. When this happens, you fail to reject the Null Hypothesis. Do we reject the Null Hypothesis? 1) Value of the sample mean = 5.2 2) “Test value” = 8; Population mean 3) “Mean difference” = –2.8; H0: College students sleep the same or more than most folks Decision based on t score and p value T score is large = 7.799 p value (probability of this being by chance) is very low < 0.001 Answer: YES / NO? Fail to reject the Null Hypothesis? 1) Value of the sample mean = 7.5 2) “Test value” = 8; Population mean 3) “Mean difference” = –0.500 H0: College students sleep the same or more than most folks Decision based on t score and p value t score is small = 2.236 p value (probability of this being by chance) is very high 0.052 Answer: YES / NO? We Conclude That… Big t value and small p value Reject Null Hypothesis Significant difference Sample comes from a different population Group is different from Null Hypothesis mean Small t value and big p value Fail to reject Null Hypothesis Data set is not significant Sample comes from the same population & mean varies by chance Group is not different from Null Hypothesis Errors in Hypothesis Testing