Based on the data, is the average sale amount statistically the same for the A, B, and C groups?
I performed t.test on AB, BC, CA. for CA, p-value>0.05, so I concluded for CA, we can't reject null hypothesis, and average may be same.
H1- alternative hypothesis was - true difference in means between group 36-45 and group 46-50 is not equal to 0
My Question is - Did I do this correctly or is there another way to check the hypothesis for three groups
If the population means of the groups are denoted mu_A, mu_B, and mu_C, then you are actually interested in the single joint null hypothesis: H_0: mu_A=mu_B=mu_C. The problem with conducting three pairwise test is the fact that it is difficult to control the probability of the type I error. That is, how do you know that three test at a significance level of 5% will still reject the H_0 above with 5% probability if this H_0 is true?
The test you are looking for is called an Analysis of Variance (ANOVA) test. It will provide a single test statistic and a single p-value to test the hypothesis above. If you search for "ANOVA statistical test", then Google will suggest many explanations (and probably also appropriate commands to do the analysis in R). I hope this helps.
