Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions.
Understanding
- I can explain why a test for a mean uses a t-distribution with n − 1 degrees of freedom and not the standard normal curve. (Guide: “The test statistic”; Practice Q2, Q7)
- I can explain that a matched-pairs test is a one-sample t-test on the differences, with n equal to the number of pairs. (Guide: Worked example 2; Practice Q6)
- I can explain why failing to reject H₀ does not show that H₀ is true. (Guide: “Decision and conclusion”; Practice Q4, Q7)
Calculation
- I can calculate the t test statistic from summary statistics or raw data, using the standard error s / √n. (Guide: Worked example 1; Practice Q1, Q5)
- I can find the p-value with technology for a left-tailed, right-tailed or two-sided alternative. (Guide: “Finding the p-value”; Practice Q2)
- I can use a t-table to find a range for a p-value, using the next smaller df when my df is missing. (Guide: Worked example 3)
- I can find the differences, x̄d and sd for matched pairs and check the conditions on the differences. (Guide: Worked example 2; Practice Q6)
Reasoning
- I can interpret a p-value in context, starting from the assumption that the true mean equals μ₀. (Guide: “Interpreting the p-value”; Practice Q3, Q5)
- I can make a decision by comparing the p-value with the α chosen in advance, using both numbers. (Guide: “Decision and conclusion”; Practice Q4)
- I can write a non-definitive conclusion about the true mean or mean difference of the population, in terms of Hₐ, and use it to answer the investigative question. (Guide: Worked examples 1 and 2; Practice Q5, Q6)
- I can find and correct errors in another student’s test. (Practice Q7)
All ticked? Move on to Topic 4.6, Sampling Distributions for the Difference Between Two Sample Means, or return to the course roadmap.