Let's perform a one sample t-test: In the population, the average IQ is 100. 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 with a standard deviation of 20. Did the medication affect intelligence? Use alpha = 0.05.

Steps for One-Sample t-Test |
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1. Define Null and Alternative Hypotheses 2. State Alpha 3. Calculate Degrees of Freedom 4. State Decision Rule 5. Calculate Test Statistic 6. State Results 7. State Conclusion |

Let's begin.

1. Define Null and Alternative Hypotheses

Figure 1. |
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2. State Alpha

Alpha = 0.05

3. Calculate Degrees of Freedom

df = n - 1 = 30 - 1 = 29

4. State Decision Rule

Using an alpha of 0.05 with a two-tailed test with 29 degrees of freedom, we would expect our distribution to look something like this:

Figure 2. |
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Use the t-table to look up a two-tailed test with 29 degrees of freedom and an alpha of 0.05. We find a critical value of 2.0452. Thus, our decision rule for this two-tailed test is:

If t is less than -2.0452, or greater than 2.0452, reject the null hypothesis.

5. Calculate Test Statistic

Figure 3. |
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6. State Results

t = 10.96

Result: Reject the null hypothesis.

7. State Conclusion

Medication significantly affected intelligence, t = 10.96, p < 0.05.