Questions: For a study with a related-samples design and 30 participants in which each participant is measured twice (repeated measures), what is the critical value (table value)? Assume a two-tailed test with a = 0.05 2.048 2.045 1.699 2.042

For a study with a related-samples design and 30 participants in which each participant is measured twice (repeated measures), what is the critical value (table value)? Assume a two-tailed test with a = 0.05
2.048
2.045
1.699
2.042

Transcript text: For a study with a related-samples design and 30 participants in which each participant is measured twice (repeated measures), what is the critical value (table value)? Assume a two-tailed test with a = 0.05 2.048 2.045 1.699 2.042

Solution

Solution Steps

To find the critical value for a related-samples design with 30 participants measured twice, we need to determine the degrees of freedom, which is the number of participants minus one. Then, we use the t-distribution to find the critical value for a two-tailed test with a significance level of 0.05.

Step 1: Determine Degrees of Freedom

For a related-samples design with \( n = 30 \) participants, the degrees of freedom (df) is calculated as: \[ df = n - 1 = 30 - 1 = 29 \]

Step 2: Identify Significance Level

The significance level for a two-tailed test is given as \( \alpha = 0.05 \).

Step 3: Calculate Critical Value

Using the t-distribution, the critical value for \( df = 29 \) and \( \alpha = 0.05 \) is found to be: \[ \text{Critical Value} \approx 2.0452 \]