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Aim: How do we find the critical values of a z test? HW#7: last slide SPSS Assignment Due Monday

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Choosing Significant Level The researcher decides what level of significance to use It does not always have to be at a 0.05 or 0.01 level It can be any level, depending on the seriousness of the type I error. After a significance level is chosen, a critical value is selected from a table for the appropriate test If a z test is used, for example, the z table is consulted to find the critical value The critical value determines the critical and noncritical regions

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Definitions Critical Value: separates the critical region from the noncritical region – The symbol for critical value is C.V. Critical or Rejection Region: is the range of values of the test values that indicates that there is a significant difference and that the null hypothesis should be rejected Noncritical or nonrejection region: the range of values of the test value that indicates that the difference was probably due to chance and that the null hypothesis should be rejected

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Finding the Critical Value The critical value can be on the right side of the mean or on the left side of the mean for one-tailed test. – Its location depends on the inequality sign of the alternative hypothesis

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One Tailed Test One Tailed Test: indicates that the null hypothesis should be rejected when the test value is in the critical region on one side of the mean A one tailed test is either a right-tailed test or left-tailed test, depending on the direction of the inequality of the alternative hypothesis

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To obtain the critical value, choose an alpha level Example: Suppose the researcher choose a significant level of.01. Then the researcher must find a z value such that 1% of the area falls to the right of the z value and 99% falls to the left of the z value

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To obtain the critical value, choose an alpha level Next, the researcher must find the value using the z table closest to.4900….the critical value is 2.33 since that value gives the area closest to.4900

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Critical and Noncritical Regions for.01

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Two Tailed Test Two Tailed Test: the null hypothesis should be rejected when the test values is in either of the two critical regions For a two-tailed test, the critical region must be split into two equal parts.

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To obtain the critical value, choose an beta level If significant level is.01, then one-half of the area, or.005 must be the right of the mean and one-half must be to the left of the mean.

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To obtain the critical value, choose an beta level In this case, the area to be found on the table is.4950 The critical values are +2.58 and -2.58

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Two-Tailed Test

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Finding the Critical Values for Specific alpha values Step1 : Draw the figure and indicate the appropriate are a.If the test is left-tailed, the critical region, with an area equal to alpha, will be on the left side of the mean b.If the test is right-tailed, the critical region, with an area equal to alpha will be on the right of the mean c.If the test is two-tailed alpha must be divided by 2; and one-half of the area will be to the right of the mean and one-half will be to the left of the mean Step 2: For a one-tailed test, subtract the area in the critical region from.5000, since z table gives the area under the curve between 0 and z to the right of 0. For a two tailed test, subtract the area from.500 Step 3: Find the area in z table corresponding to the value obtained in step 2. If the exact value cannot be found in the table, use the closest value. Step 4: Find the z value that corresponds to the area. This will be the critical value Step 5: Determine the sign of the critical value for a one-tailed test a.If the test is left-tailed, the critical value will be negative b.If the test is right-tailed the critical value will be positive c.For a two-tailed test, one value will be positive and the other negative

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Homework #7 1.Find the critical value(s) for each situation and draw the appropriate figure, showing the critical region. a.A left-tailed test with significant level.10 b.A two-tailed test with significant level.02 c.A right-tailed test with significant level.005

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