Module 28 // Relationship between CI and Sig Tests

The results of a confidence interval and significance test should agree as long as:

1. we are making inferences about means 2. the significance test is two-sided 3. Unknown This will get you 0.67 out of 1 points. Take your best guess.

A test of Ho:mu=542 vs Ha: mu not=542 resulted in a p-value of 0.09. We can predict that, using the same data set: A. the 90% CI for mu {will // will not } include 542 B. the 95% CI for mu {will // will not } include 542 C. the 99% CI for mu {will // will not } include 542

A = Will not B = Will C = Will

A test of Ho:mu=3 vs Ha: mu not=3 resulted in a p-value of 0.13. We can predict that, using the same data set: A. the 90% CI for mu {will // will not } include 3 B. the 95% CI for mu {will // will not } include 3 C. the 99% CI for mu {will // will not } include 3

A. Will B. Will C. Will as p-value is greater than all of the levels of significance 0.1; 0.05; 0.01, therefore, ALL intervals WILL include 3.

When looking at the results of a 90% confidence interval, we can predict what the results of the two-sided significance test will be:

Answer is at alpha 0.10 (look at t-table and find ___ & * by 2) So 0.05 * 2 = 0.10

When looking at the results of a 95% confidence interval, we can predict what the results of the two-sided significance test will be:

Answer is at alpha = 0.05 (look at t-table find ___ and & * by 2) So 0.025 * 2 = 0.05

Suppose that you had consumer group wanted to test to see if the weight of participants in a weight loss program changed (up or down). They computed a 95% confidence interval of the result ( - 4.977, 2.177). Suppose that we had a significance test with the following hypothesis: Ho: population mean weight loss = 0 Ha: population mean weight loss does not equal 0 What do we know about the p-value for the test?

It would be greater than 0.05. Make sure to check signs !!! Trick Question

In 2008, the General Social Survey asked 1,335 people how many hours a day did they watch television. A 95% confidence interval for the average amount of hours that Americans watch television per day is between 2.70 and 2.95. What can we conclude about the significance test of Ho:mu=2.5 vs. Ha: mu does not equal 2.5?

It's p-value will be smaller than .05 TRUE - since the 95% CI does NOT include 2.5, we would reject Ho: mu = 2.5 at alpha = .05, hence the p-value must be smaller than .05.