Im having difficulties understanding the connection between the p-values and CIs. Some of these results in the picture seem to be inconsistent. Starting with G1:
divide the two sample means in order to acquire a t statistic which will then state that the difference between these two sample means represents the population mean.
The H0 is: the difference between the two sample means is equal to 0 (there is no difference), with a p-value of 0.05. If the p-value is below 0.05 we reject the null hypothesis. If it's greater than 0.05 we fail to reject the hypothesis. So,
G1 has a p-value 0.02<0.05 --> we reject the null hypothesis
We can't find a 0 in the confidence interval so we reject the null hypothesis. The population means are not equal. Fining a 0 in the interval would mean that we have found the H0 to be true.
G2--> CI has a 0, p-value is 0.07>0.05 --> we fail to reject the H0.
G3--> there is no 0 in CI --> we reject, and 0.09>0.05 we accept the H0 --Inconsistency! We would need to have a confidence interval including a 0.
G4--> CI doesn't involve a 0 indicating there is a difference between the means--rejecting H0; 0.13 > 0.05 we accept the H0. Inconsistency! A better p-value would be more close to 0.05?
Thanks for bearing with me and having read the whole text! You can open the screenshot i "interpreted" here 2
