Let's perform a one sample z-test: In the population, the average IQ is 100 with a standard deviation of 15. A team of scientists wants to test a new medication to see if it has either a positive or negative effect on intelligence, or no effect at all. A sample of 30 participants who have taken the medication has a mean of 140. Did the medication affect intelligence, using alpha = 0.05?

Steps for One-Sample z-Test |
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1. Define Null and Alternative Hypotheses 2. State Alpha 3. State Decision Rule 4. Calculate Test Statistic 5. State Results 6. State Conclusion |

Let's begin.

1. Define Null and Alternative Hypotheses

Figure 1. |
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2. State Alpha

Using an alpha of 0.05 with a two-tailed test, we would expect our distribution to look something like this:

Figure 2. |
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Here we have 0.025 in each tail. Looking up 1 - 0.025 in our z-table, we find a critical value of 1.96. Thus, our decision rule for this two-tailed test is:

If Z is less than -1.96, or greater than 1.96, reject the null hypothesis.

4. Calculate Test Statistic

Figure 3. |
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5. State Results

Z = 14.60

Result: Reject the null hypothesis.

6. State Conclusion

Medication significantly affected intelligence, z = 14.60, p < 0.05.