2. Single Sample t-test Purpose: Compare a sample mean to a hypothesized population mean. Design: One group

3. Why not a z-test? The z test requires you to know the , but you usually don’t know it. If you don’t know , your best estimate of it is s x. When you use s x instead of , you are doing a t-test.

4. Comparing z and t

5. The t distribution is symmetrical but flatter than a normal distribution. The exact shape of a t distribution depends on degrees of freedom

6. normal distribution t distribution

7. Degrees of Freedom Amount of information in the sample Changes depending on the design and statistic For a one-group design, df = N-1 The last score is not “free to vary”

8. Assumptions 1. Independent observations. 2. Population distribution is symmetrical. 3. Interval or ratio level data.

9. Example An achievement test is designed to have a population mean of 50. A sample of 49 people take the test, and their mean is 56, with a sample standard deviation of 14. Is there a significant difference between means?

10. STEP 1: Calculate the standard error of the mean.

11. STEP 2: Calculate the t.

12. STEP 3: Find the critical value of t using the t table. df = N-1 df = 49-1 = 48 two-tailed  =.05 t-crit = 2.021 (for 40 df, next lowest) lowest)

13. STEP 4: Compare t to t-crit. If t is equal to or greater than t-crit, it is significant. (For 2- tailed tests, ignore the sign). t = 3.00, t-crit = 2.021 Reject Ho; significant

14. APA Format Sentence A single-sample t-test showed that the mean of the class was significantly different from the mean of the population, t (48) = 3.00, p <.05.