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

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Hypothesis Testing with z

Hypothesis Testing with zUsing the Normal Distributionin a Hypothesis Test

Example 1Example 1, continuedExample 1 initial directionStep 1. State the hypothesesStep 2. Determine the Critical ValueStep 2. Determine the Critical Value

Step 2. Determine the Critical Value

Step 3. Compute the Test StatisticFormulaIn this example,

Step 4. Make a DecisionIf your Test Value is insidethe Critical Region,then REJECT the null hypothesis.If your Test Value is outside the CriticalRegion, then FAIL TO REJECT the H0.Here, we FAIL TO REJECT.

A remark about our decisionStep 5. Plain English conclusionThe 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.Example 2Example 2 remarksWe 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 toolWe want the Central Limit Theorem to tell us that these results are too good to be mere coincidence.

14Example 2 initial directionStep 1. State the hypothesesStep 2. Determine the Critical ValueStep 2. Determine the Critical Value

Step 2. Determine the Critical ValueWhat z value is at the boundary? Lookup in printed tables.Or use TI-84 invNorm(.99)THE CRITICAL VALUE is 2.33

Step 3. Compute the Test StatisticFormulaIn this example,

Step 4. Make a DecisionIf your Test Value is inside the CriticalRegion, then REJECT the null hypothesis.If your Test Value is outside the CriticalRegion, then FAIL TO REJECT the H0.Here, we REJECT THE NULL HYPOTHESIS.

Remarks about our decisionIf our students had scored 80 or 81 or so, it would have been higher, but not significantly higher.The Central Limit Theorem would have explained it as just variations in sampling.But we have something really big here, something improbable according to the C.L.T.Less than 1% chance this result was just luck.Step 5. Plain English conclusionThe 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 significantly higher than the statewide average in a recent examination.Example 3Example 3 initial directionStep 1. State the hypothesesStep 2. Determine the Critical ValueStep 2. Determine the Critical Values

Step 3. Compute the Test StatisticFormulaIn this example,

Step 4. Make a DecisionIf your Test Value is inside the CriticalRegion, then REJECT the null hypothesis.If your Test Value is outside the CriticalRegion, then FAIL TO REJECT the H0.Here, we FAIL TO REJECT THE NULL HYPOTH.

Remarks about our decisionThe 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.

Step 5. Plain English conclusionThe 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.

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