STAT 111 Lecture Notes - Lecture 16: Confidence Interval, Null Hypothesis, Statistical Hypothesis Testing

• School: University of Vermont
• Department: Statistics
• Course: STAT 111
• Professor: Jacob William Martin

Document Summary

Z* = standard normal z* is always the same, regardless of the data. Confidence interval : statistic +/- z* x standard error. Z-statistic : (statistic - null) / standard error z* comes from n(0,1) and z-statistic is compared to n(0,1) for p-value. The larger the sample size, the smaller the error. P-hat ~ n (p, p(1-p) / n) A normal distribution is a good approximation as long as np > 10 and n(1-p) > 10. Margin of error : ci = statistic +/- margin of error. Given this formula for margin of error, solve for n. You can choose your sample size in advance, depending on your desired margin of error. When we have no idea what the value of p-hat is, will be a conservative value of. This will give us the largest sample necessary. For hypothesis testing, we want the distribution of the sample proportion assuming the null hypothesis is true.