STAT 302 502 Week 10 10 30 Type I Error but H we reject H 0 Type II Error 0 is actually true is actually false but H we do not reject H 0 0 when H we want to make sure that we are not accepting H 0 when H is false 0 is false 0 0 we also want to make sure that we are rejecting H t distributions when we are using t distributions population standard deviation is unknown and we are also assuming that the population is Normal for t distributions we use we use the standard error because we do not know the population SD after calculating the t score we use df n 1 and the confidence level usually 95 and refer to the t distribution table to find the p value when we are using t distributions we want to make sure that we are using df n 1 instead of just using the sample size n sometimes the p value will be between a range of numbers ie 0 02 p value 0 01 based on whether the p value is greater than or less than we can either reject or fail to reject our hypotheses REMEMBER the p value is not the probability that H0 is true the p value refers to the sample statistic not the population parameter p value is the probability of observing a sample statistic that is extreme given that H is true 0 Making Conclusions if p value is LARGER than we fail to reject H if p value is SMALLER than we reject H 0 0 10 H 0 for us to get a sample value of 10 rare value for a two sided test of the null hypothesis p The Exercise was found to be 0 06 Therefore using the same data Confidence Level of 95 0 05 p 0 06 0 05 Therefore the data is not statistically significant and we fail to reject our null hypothesis This is because the confidence interval would contain the value 10 if our null hypothesis was true and getting a value of 10 is not that extreme Confidence Level of 90 0 10 p 0 06 0 10 Therefore the data is statistically significant and we reject our null hypothesis This is because the confidence interval would not contain the value 10 and it was really 0 H A we made a Type II error p 0 97 The test results in a P value of 0 12 In reality the p Suppose that a manufacturer is testing one of its machines to H 0 Exercise make sure that the machine is producing more than 97 good parts 0 97 and machine is producing 99 good parts What probably happens as a result of our testing Answer We failed to reject the null hypothesis because the data was not statistically significant But in actuality the null hypothesis is false and the alternative hypothesis is true and by failing to reject a FALSE H We test it on a fleet of cars with Suppose that a device advertised to increase a car s gas not H 0 Exercise mileage actually does not work effective and our data results in a P value of 0 004 With 5 level of significance what probably happens as a result of our experiment Answer The p value 0 004 was smaller than the significance level 0 05 We rejected the null hypothesis because the data was statistically significant we However the device doesn t actually work and by rejecting a TRUE H 0 made a Type I error
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