Chapter 4 One-Group t-Test for the Mean Chapter focuses: (1)

One of the most popular and most helpful statistical tests The formula for the one-group t-test: 𝑥= 𝑋 −𝜇 𝑆 𝑋 Where 𝑆 𝑋 (i.e., s.e.) = 𝑠 𝑛

4.1 The 7 STEPS for Hypothesis-Testing Using the One-Group t-Test 4.1.1 STEP 1: State the Null Hypothesis and the Research Hypothesis 4.1.2 STEP 2: Select the Appropriate Statistical Test (The t-test is selected in this chapter.) 4.1.3 STEP 3: Decide on a Decision Rule for the One-Group t-Test 4.1.4 STEP 4: Calculate the Formula for the One-Group t-Test 4.1.5 STEP 5: Find the Critical Value of t in the t-Table in Appendix E 4.1.6 STEP 6: State the Result of Your Statistical Test 4.1.7 STEP 7: State the Conclusion of Your Statistical Test in Plain English!

STEP 1: State the Null Hypothesis and the Research Hypothesis For 7-point scales with 1 = poor and 7 = excellent, Null hypothesis H0: μ = 4 Research hypothesis H1: μ ≠ 4 STEP 2: Select the Appropriate Statistical Test In this chapter, the one-group t-test will be selected. 4.1.3 STEP 3: Decide on a Decision Rule for the One-Group t-Test (a) If the absolute value of t is less than the critical value of t, accept the null hypothesis. (b) If the absolute value of t is greater than the critical value of t, reject the null hypothesis and accept the research hypothesis.

STEP 4: Calculate the Formula for the One-Group t-Test 𝑥= 𝑋 −𝜇 𝑆 𝑋 , where 𝑆 𝑋 (i.e., s.e.) = 𝑠 𝑛 This formula makes the following assumptions about the data (Foster et al. 1998): (1) The data are independent of each other (i.e., each person receives only one score), (2) the population of the data is normally distributed, and (3) the data have a constant variance (note that the standard deviation is the square root of the variance). STEP 5: Find the Critical Value of t in the t-Table in Appendix E

4.1.6 STEP 6: State the Result of Your Statistical Test There are two possible results when you use the one-group t-test, and only one of them can be accepted as “true.” Either: Since the absolute value of t that you found in the t-test formula is less than the critical value of t in Appendix E, you accept the null hypothesis. Or: Since the absolute value of t that you found in the t-test formula is greater than the critical value of t in Appendix E, you reject the null hypothesis, and accept the research hypothesis. 4.1.7 STEP 7: State the Conclusion of Your Statistical Test in Plain English! Try to summarize the result of your statistical test in simple English that is both concise and accurate so that someone who has never had a statistics course (such as your boss, perhaps) can understand the result of your test.

4.2 One-Group t-Test for the Mean