.03. test if the normal popu- and a treat- e treatment is age of 4 msec. vith a two- ,what is the researcher uses size influ- at all other

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### Statistical Analysis in Research

#### Problem 17

**Scenario:**

A sample of \( n = 40 \) is selected from a normal population with \( \mu = 75 \) msec and \( \sigma = 12 \), and a treatment is administered to the sample. The treatment is expected to increase scores by an average of 4 msec.

**Tasks:**

**a. Two-Tailed Hypothesis Test:**

If the treatment effect is evaluated with a two-tailed hypothesis test using \( \alpha = .05 \), what is the power of the test?

**b. One-Tailed Hypothesis Test:**

What is the power of the test if the researcher uses a one-tailed test with \( \alpha = .05 \)?

#### Problem 18

**Scenario:**

Briefly explain how increasing sample size influences each of the following. Assume that all other factors are held constant.

---

**Note:** For detailed statistical analysis including power calculations, reference corresponding statistical tables or software. Understanding factors such as sample size, test type (one-tailed vs. two-tailed), and significance level \( \alpha \) helps in accurately interpreting outcomes.
Transcribed Image Text:### Statistical Analysis in Research #### Problem 17 **Scenario:** A sample of \( n = 40 \) is selected from a normal population with \( \mu = 75 \) msec and \( \sigma = 12 \), and a treatment is administered to the sample. The treatment is expected to increase scores by an average of 4 msec. **Tasks:** **a. Two-Tailed Hypothesis Test:** If the treatment effect is evaluated with a two-tailed hypothesis test using \( \alpha = .05 \), what is the power of the test? **b. One-Tailed Hypothesis Test:** What is the power of the test if the researcher uses a one-tailed test with \( \alpha = .05 \)? #### Problem 18 **Scenario:** Briefly explain how increasing sample size influences each of the following. Assume that all other factors are held constant. --- **Note:** For detailed statistical analysis including power calculations, reference corresponding statistical tables or software. Understanding factors such as sample size, test type (one-tailed vs. two-tailed), and significance level \( \alpha \) helps in accurately interpreting outcomes.
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