If the sample proportion is greater than 60 or less

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If the sample proportion is greater than .60 or less than .40, we reject the null. So if we got 56 pink carnations, to take a specific example, we’d accept the null.
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This is the Picture 0.34 0.42 0.50 0.58 0.66 0 1 2 3 4 5 6 7 8 Normal Density Distribution of Sample Proportion of Pink Carnations when Null Hypothesis is true. Accept Reject Reject .40 .60 .56 .025 .025
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Other ways to do the test As in the case of Greater-than tests, there are two other ways to perform the test. Compare observed z-values to critical z-value(s). Compare a p-value to α . Let’s repeat the test, using the z-value technique.
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-3 -2 -1 0 1 2 3 0.0 0.1 0.2 0.3 0.4 Normal Density Distribution of Sample Proportion of Pink Carnations when Null Hypothesis is true. (Rescaled to z-scores) Acceptance and Rejection Regions in z-values Accept Reject Reject 2 α 2 α -z α /2 z α /2
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Computing an observed z Our sample outcome is that 56 of 100 offspring are pink, so the observed z is 1.20. Note we use .50, not .56, in computing the standard deviation. This is because α is a probability given the null is true , and the null says p = .50. For α = .05, we accept H 0 . .025 .025 .56 .50 .5 .5 100 1.20 1.96 1.20 1.96 obs obs z z z z = × = = − < < =
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