Suppose I was not sure if the dice were fair, or I didn't know the population mean I could construct a confidence interval using sample mean x I there is a 95% probability that will be included in the interval of sample mean plus or minus 1.96 standard deviations: 33 / 37 Introduction Random sampling sampling distribution using CLT I Suppose in my sample I have x = 6.45, and I can say there's 95% probability that is in the interval [6.45 1.96 n ]. I CI: [5.78, 7.12] I note that some people will get a CI that doesn't actually include the true mean, because 5% of the time we will be wrong (these are probabilities and they can be different from the realizations) I Discussion question: How will your CI change if in you rolled the pair of dice 500 times?

q. How does confidence interval change, based on n, x and ?