7. The Relationship between Confidence Intervals and Tests of Significance

d. explain a decision rule, the power of a test, and the relation between confidence intervals and hypothesis tests;

What is a confidence interval? A confidence interval is a range of values within which it is believed that a certain unknown population parameter (often the mean) will fall with a certain degree of confidence. The percentage of confidence is denoted (1 - \alpha)%.

What is a test of significance? A test of significance is a test to ascertain whether or not the value of an unknown population parameter is as stated by an individual or institution. This test is carried out at a significance level of \alpha, which determines the size of the rejection region.

What is a test of significance testing for? What is the math formula? - We are testing to see the likelihood that the z-value will be less than the test statistic. - \(\mu_0 < \bar{x} - \frac{(z_{a/2})(\sigma)}{\sqrt{n}}\)

When conducting a significance test and the confidence interval contains the value of the unknown population parameter as hypothesized in the null hypothesis (H_0), is the null hypothesis rejected or not? Not rejected

Given the following info, is the p-value > or < 0.05? H_0:\mu = 50, H_a:\mu != 50, normal population with \sigma = 6. Standard confidence interval for the mean is (51.3, 54.7).