STA 238 University of Toronto W9 Statistics Questionnaire

1. This is a question I suddenly started thinking about after I finished my proposal. If we want to get the CI for the mean value of sth, and from our sample we can already see the distribution of it and many key points of it like the mean value, standard deviation value, min, and max after drawing the boxplot of it and histogram of it. However, if we already find that it is not normally distributed from the shape of our plot, is it reasonable or scientifically rigorous enough if we just directly skip the Goodness of fit test for it, and choose to use bootstrap CI later since from the histogram shape it is not normally distributed? Thanks in advance!

2. When we are doing a hypothesis test, we know that we cannot find the probability of getting exactly the observed outcome. Why is it happened? Is it because there are so many probabilities?

3. .I wonder if we can determine the p-value is the probability for more extreme outcomes than the current outcome? Because assuming that the distribution of the various outcomes we consider is normal, then the values that are more extreme than a certain value should be two-tailed, but we sometimes only consider one tail, so can the p-value still be counted as the probability of more extreme results?

4. post one questions you want to ask based on the pdf