Do teachers’ self-fulfilling prophecies boost student IQ? Researchers randomly selected 50 students and told their teachers that these students scored very highly on a new intelligence test and are expected to be special when they get older. Student IQs in general for this grade level are μ= 100 and σ=15. After one year, researchers tested the 50 students’ IQs and found that the students’ IQs were on average=105. Did teacher expectations change students’ IQs?

`Should you run a one-tailed or two-tailed test? Why?`

In this case, it is enough to run a (right) one-tailed t-test because we are testing the hypothesis only in one direction. We are not interested in whether teachers’ self-fulfilling prophecies will either positively or negatively affect student IQ.

`What are the null and alternative hypotheses? What will be the alpha level? `

Ho: Teachers’ self-fulfilling prophecies don’t boost student IQ

H1: Teachers’ self-fulfilling prophecies boost student IQ

a: 0.05 (because it’s a commonly used alpha level)

Conduct your hypothesis test!

```
State the hypothesis(Ho, H1) and select the alpha level (a) [already done above]
Set the decision criteria by locating the criteria region (Zcritical)
```

Z critical = 1.64 (According to the table)

Compute the test statistic (σM and z score for sample M)

σM = 15/√50 = 15/7.07 = 2.12 z = (105 – 100) / σM = 2.36

Make a decision (statistically significant or not.)

2.36>1.64 statistically significant, rejecting H0

Interpret findings in light of hypotheses [question be

low this one]

`Is the difference significant? Explain the finding in plain English. Refer back to your original hypothesis in your explanation. `

The results are statistically significant because the Z score = 2.36, meaning that it is located in the region over the z critical value, which is 1.64. If it had been below this value, then H0 would not have been rejected. If a student’s average IQ after one year was not 105 but 103 or lower, then the results would be rejected because, in this case, the Z score would be below the 1.64 z critical value. Hence, it can be concluded that teacher expectations are correlated with changes in students’ IQ. Another important thing that should be mentioned is that correlation doesn’t mean that there is causation. In other words, it is possible that statistically significant results were influenced not by teachers’ self-fulfilling prophecies but by other factors. Hence, a control group should be used to compare the results of students from the control group and the experimental group.