Download Relationship between Hypothesis Testing and Confidence Intervals in Statistical Analysis and more Exams Statistics in PDF only on Docsity! Stat 4473 – Data Analysis Relationship between hypothesis testing and confidence intervals (Homework on back side) Suppose the significance level is preset at ". The relationship between hypothesis testing and confidence intervals is described below. (1) Ho: population parameter = hypothesized value H1: population parameter … hypothesized value Reject Ho in favor of H1 if the hypothesized value is outside the 100(1 - ")% confidence interval (two-sided) for the population parameter Example: Ho: µ = 5 H1: µ… 5 ! If a 95% confidence interval for : doesn’t contain 5, then we know the p-value for the test is less than .05. If a 95% confidence interval for : does contain 5, then we know the p-value is greater than .05 ! If a 90% confidence interval for : doesn’t contain 5, then we know the p-value for the test is less than .10. If a 90% confidence interval for : does contain 5, then we know the p-value for the test is greater than .10. ! If a 99% confidence interval for : doesn’t contain 5, then we know the p-value for the test is less than .01. If a 99% confidence interval for : does contain 5, then we know the p-value for the test is greater than .01. (2) Ho: population parameter = hypothesized value H1: population parameter > hypothesized value Reject Ho in favor of H1 if the hypothesized value is outside the 100(1 - ")% lower confidence interval (one-sided) for the population parameter. A 100(1 - ")% lower confidence interval is an interval of the form (left endpt., + 4). It says that we are 100(1 - ")% confident that the population parameter is at least as large as the left endpoint. (It gives just a lower limit.) All the margin of error is on the right side. (3) Ho: population parameter = hypothesized value H1: population parameter < hypothesized value Reject Ho in favor of H1 if the hypothesized value is outside the 100(1 - ")% upper confidence interval (one-sided) for the population parameter. A 100(1 - ")% upper confidence interval is an interval of the form (!4, right endpt). It says that we are 100(1 - ")% confident that the population parameter is no larger than the right endpoint. (It gives just an upper limit.) All the margin of error is on the left side.
