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

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  • Slide 1
  • Hypothesis Testing with t Using the Normal Distribution t Distribution in a Hypothesis Test
  • Slide 2
  • When and Why t Distribution & t instead of Normal Distribution & z Normal Distribution and zt Distribution and t
  • Slide 3
  • Example 1
  • Slide 4
  • Example 1, continued
  • Slide 5
  • Example 1 initial direction
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  • Step 1. State the hypotheses
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  • Step 2. Determine the Critical Value
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  • Slide 9
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  • d.f.One tail, = 0.05 451.679 501.676
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  • About that t table d.f.One tail, = 0.05 451.679 501.676
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  • Step 3. Compute the Test Statistic FormulaIn this example,
  • Slide 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.
  • Slide 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.
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  • A remark about our decision
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  • Step 5. Plain English conclusion The conclusion has to be suitable for a general audience. They dont want to hear any Statistics lingo. Say something that a journalism school major could read in a news report. Heres what we can say: There is NOT enough evidence to conclude that these rivets are SIGNIFICANTLY weaker than the required strength.
  • Slide 17
  • Example 2
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  • Example 2 remarks We scored higher, thats 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.
  • Slide 19
  • Example 2 initial direction
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  • Step 1. State the hypotheses
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  • Step 2. Determine the Critical Value
  • Slide 22
  • Slide 23
  • d.f.One tail, 0.01 382.434 402.429
  • Slide 24
  • Step 3. Compute the Test Statistic FormulaIn this example,
  • Slide 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.
  • Slide 26
  • Step 5. Plain English conclusion The conclusion has to be suitable for a general audience. They dont want to hear any Statistics lingo. Say something that a journalism school major could read in a news report. Heres 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.
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  • Example 3
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  • Example 3 initial direction
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  • Step 1. State the hypotheses
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  • Step 2. Determine the Critical Value
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  • Step 2. Determine the Critical Values d.f.Two tails, =0.05 342.032 362.028
  • Slide 32
  • Step 3. Compute the Test Statistic FormulaIn this example,
  • Slide 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.
  • Slide 34
  • Remarks about our decision The racing fans at our track were certainly younger than the supposed average age of 55. But it wasnt 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.
  • Slide 35
  • Step 5. Plain English conclusion The conclusion has to be suitable for a general audience. They dont want to hear any Statistics lingo. Say something that a journalism school major could read in a news report. Heres what we can say: We cant disagree that the average age of a horse racing fan really is 55 years old, despite a little bit of evidence to the contrary.