1. Hypothesis Testing with t Using the Normal Distribution t Distribution in a Hypothesis Test

2. When and Why t Distribution & t instead of Normal Distribution & z Normal Distribution and zt Distribution and t

3. Example 1

4. Example 1, continued

5. Example 1 initial direction

6. Step 1. State the hypotheses

7. Step 2. Determine the Critical Value

10. d.f.One tail, αα = 0.05 451.679 501.676

11. About that t table… d.f.One tail, αα = 0.05 451.679 501.676

12. Step 3. Compute the Test Statistic FormulaIn this example,

13. Step 4. Make a Decision If your Test Value is inside the Critical Region, then REJECT the null hypothesis. If your Test Value is outside the Critical Region, then “FAIL TO REJECT” the H 0. Here, we “FAIL TO REJECT”.

14. A remark about z vs. t When we did this as a z problem, the critical z value was -1.651. When we did this as a t problem, the critical t value was -1.677. Other than that, the procedure was exactly the same.

15. A remark about our decision

16. Step 5. Plain English conclusion The conclusion has to be suitable for a general audience. They don’t want to hear any Statistics lingo. Say something that a journalism school major could read in a news report. Here’s what we can say: “There is NOT enough evidence to conclude that these rivets are SIGNIFICANTLY weaker than the required strength.”

17. Example 2

18. Example 2 remarks We scored higher, that’s for sure. 83.15 vs. 79.68 statewide. But we have to be careful before issuing a press release or using these results as a recruiting tool We want the Central Limit Theorem to tell us that these results are too good to be mere coincidence.

19. Example 2 initial direction

20. Step 1. State the hypotheses

21. Step 2. Determine the Critical Value

23. d.f.One tail, α0.01 382.434 402.429

24. Step 3. Compute the Test Statistic FormulaIn this example,

25. Step 4. Make a Decision If your Test Value is inside the Critical Region, then REJECT the null hypothesis. If your Test Value is outside the Critical Region, then “FAIL TO REJECT” the H 0. Here, we just barely “Fail to Reject H0” When we did this with z, we did reject.

26. Step 5. Plain English conclusion The conclusion has to be suitable for a general audience. They don’t want to hear any Statistics lingo. Say something that a journalism school major could read in a news report. Here’s what we can say: “Darton State College EMT students scored higher than the statewide average in a recent examination, but not at a statistically significant level.”

27. Example 3

28. Example 3 initial direction

29. Step 1. State the hypotheses

30. Step 2. Determine the Critical Value

31. Step 2. Determine the Critical Values d.f.Two tails, αα=0.05 342.032 362.028

32. Step 3. Compute the Test Statistic FormulaIn this example,

33. Step 4. Make a Decision If your Test Value is inside the Critical Region, then REJECT the null hypothesis. If your Test Value is outside the Critical Region, then “FAIL TO REJECT” the H 0. Here, we “FAIL TO REJECT THE NULL HYPOTH.”

34. Remarks about our decision The racing fans at our track were certainly younger than the supposed average age of 55. But it wasn’t strong enough evidence. So we let the null hypothesis stand. We did NOT “prove” the null hypothesis. We merely collected evidence that mildly disagreed with the null hypothesis.

35. Step 5. Plain English conclusion The conclusion has to be suitable for a general audience. They don’t want to hear any Statistics lingo. Say something that a journalism school major could read in a news report. Here’s what we can say: “We can’t disagree that the average age of a horse racing fan really is 55 years old, despite a little bit of evidence to the contrary.”