Question 1185822
Here's how to conduct a hypothesis test to determine if poor readers have lower IQ scores:

**1. Hypotheses:**

*   **Null Hypothesis (H0):** Poor readers have the same average IQ as other students (μ = 105).
*   **Alternative Hypothesis (H1):** Poor readers have a lower average IQ than other students (μ < 105). This is a left-tailed test.

**2. Significance Level (alpha):** α = 0.05 (5%)

**3. Test Statistic:** Since the sample size is small (n = 30) and the population standard deviation is unknown, we use a t-test. The test statistic is:

```
t = (x̄ - μ) / (s / √n)
```

Where:

*   x̄ is the sample mean (101.5)
*   μ is the population mean under H0 (105)
*   s is the sample standard deviation (1.42)
*   n is the sample size (30)

**4. Degrees of Freedom:** df = n - 1 = 30 - 1 = 29

**5. Critical Value:** For a one-tailed (left-tailed) t-test with α = 0.05 and df = 29, we consult a t-table or calculator. The critical value is approximately t = -1.699.

**6. Decision Rule:** Reject H0 if the calculated t-statistic is less than the critical value (-1.699).

**7. Calculation:**

```
t = (101.5 - 105) / (1.42 / √30)
t = -3.5 / 0.259
t ≈ -13.51
```

**8. Conclusion:**

The calculated t-statistic (-13.51) is *less than* the critical value (-1.699). Therefore, we *reject* the null hypothesis.

**Interpretation:**

At a 5% significance level, there is sufficient evidence from the sample to conclude that poor readers have a lower average IQ than other students in the school system.