Chapter 9

# 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
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
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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