4-2 THE ONE-SAMPLE t-TEST FOR A POPULATION MEAN ACTIVITY What is a 1-sample t-test for? When we have a question about a population mean, like Sarah's overall average jump distance, we usually don't have access to all of the population values because Sarah practices a lot, doesn't necessarily record the length of every jump, and her ability includes tomorrow's jumps, which aren't in the data. So we hypothesize about what's true in general, but have to use a limited data set to make a decision. 1. a. What null and alternative hypotheses are appropriate for the coach's research question in the Pre-Activity? ylblimu ylao b. Review your Pre-Activity work summarizing the data. Do data seem to support the al- ternative or the null hypothesis? Justify your answer. c. Are you sure about your answer in b? Explain. How do we do a 1-sample t-test? We'll use the same 4-step hypothesis test procedure that we used for the hypothesis tests in Section 4-1. Since the sample size is fairly small (less than n = 100) and we have no information about the population standard deviation, then the Central Limit Theorem doesn't apply. As long as conditions are met, we can use the t-distribution to find the p-value, and the p-value helps us judge whether the data are consistent with the null hypothesis value for the population, or not.