We wish to answer the same basic question that was asked with two-tailed testing:

"How likely are we to get this sample if the null hypothesis is true?"

but we test a directional null hypothesis, as stated below:

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We have the same basic four steps of hypothesis testing:

1. State the Hypotheses:
   • Null hypothesis: Alcohol consumption does not decrease birth weight. Their weight will not be less than 18 grams (i.e., it will be equal to or greater than 18 grams). In symbols:
     
   • Alternative Hypothesis: Alcohol will decrease birth weight. The weight will be less than 18 grams. In symbols:
     
2. Define the decision method:
   • (Classic Approach: Define Decision Criterion)

   • Determine the standard error of the mean (standard deviation of the distribution of sample means) for samples of size 16. The standard error is calculated by the formula:
     
     The value is 4/sqrt(16) = 1.

   • To determine how unusual the mean of the sample we will get is, we will use the Z formula to calculate Z for our sample mean under the assumption that the null hypothesis is true. The Z formula is:
     
     Note that the population mean is 18 under the null hypothesis, and the standard error is 1, as we just calculated. All we need to calculate Z is a sample mean.

     When we get the data we will calculate Z and then look it up in the Z table to see how unusual the obtained sample's mean is, if the null hypothesis Ho is true, using a one-tailed probabililty.

3. Gather Data:
   The two experimenters got these different sets of data:

   Experiment 1	Experiment 2
   Sample Mean = 13	Sample Mean = 16.5

4. Evaluate Null Hypothesis:
   We calculate Z for each experiment, and then look up the P value for the obtained Z, and make a decision. Here's what happens for each experiment:

   Experiment 1	Experiment 2
   Sample Mean = 13 Z = (13-18)/1 = -5.0 p < .0000 Reject Ho ViSta Applet	Sample Mean = 16.5 Z = (16.5-18)/1 = -1.5 p = .0670 Do Not Reject Ho ViSta Applet

   ViSta's Report for Univariate Analysis of Experiment 1 Data.

   ViSta's Report for Univariate Analysis of Experiment 2 Data.

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