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Unformatted text preview: dical emergency requests Type I Error Because hypothesis tests are based on sample data, we must allow for the possibility of errors.
s A Type I error is rejecting H0 when it is true.
s The probability of making a Type I error when the null hypothesis is true as an equality is called the level of significance.
s Applications of hypothesis testing that only control the Type I error are often called significance tests. Type II Error
Type II Error
s A Type II error is accepting H0 when it is false.
s It is difficult to control for the probability of making a Type II error.
s Statisticians avoid the risk of making a Type II error by using “do not reject H0” and not “accept H0”. Type I and Type II Errors
Type I and Type II Errors
Population Condition Conclusion H0 True
(µ < 12) H0 False
(µ > 12) Accept H0
(Conclude µ < 12) Correct
Decision Type II Error Type I Error Correct
Decision Reject H0
(Conclude µ > 12) pValue Approach to
OneTailed Hypothesis Testing The pvalue is the probability, computed using the test statistic, that measures the support (or lack of support) provided by the sample for the null hypothesis. If the pvalue is less than or equal to the level of significance α, the value of the test statistic is in the rejection region. Reject H0 if the pvalue < α . LowerTailed Test About a Population Mean:
σ Known • pValue Approach pValue < α ,
so reject H0. α = .10 Sampling
distribution
x − µ0
z of =
σ/ n pvalue
= .0 7 2 z z = zα =
1.46 1.28 0 UpperTailed Test About a Population Mean:
σ Known • pValue Approach pValue < α ,
so reject H0. Sampling
distribution
x − µ0
z of =
σ/ n α = .04 pValue
= .0 1 1
z
0 zα = 1.75 z =
2.29 Critical Value Approach to Critical Value Approach to OneTailed Hypothesis Testing The test statistic z has a standard normal probability distribution. We can use the standard normal probability distribution table to find the zvalue with an area of α in the lower (or upper) tail of the distribution. The value of the test statistic that established the boundary of the rejection region is called the critical value for the test.
s The rejection rule is: • Lower tail: Reject H0 if z < zα
• Upper tail: Reject H0 if z > zα LowerTailed Test About a Population Mean:
σ Known • Critical Value Approach Sampling
distribution
x − µ0
z= of σ/ n Reject H0 α = .1 0 − α = −
z
1.28 Do Not Reject H0
0 z UpperTailed Test About a Population Mean:
σ Known • Critical Value Approach Sampling
distribution
x − µ0
z of =
σ/ n Reject H0 Do Not Reject H0
0 α = .0 5 zα = 1.645 z Steps of Hypothesis Testing
Steps of Hypothesis Testing
Step 1. Develop the null and alternative hypotheses.
Step 2. Specify the level of significance α.
Step 3. Collect the sample data and compute the test statistic.
pValue Approach
Step 4. Use the value of the test statistic to compute the pvalue.
Step 5. Reject H0 if pvalue < α. Steps of Hypothesis Tes...
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 Spring '09
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