Question

The following are verbal SAT scores of hypothetical students who were forced to take the test under adverse conditions (e.g., construction noises, room too warm, etc.): 510, 550, 410, 530, 480, 500, 390, 420, 440. Do these scores suggest that the adverse conditions really made a difference (at the .05 level)? Report your p value.

Answer 1

To determine whether the adverse conditions made a significant difference in the verbal SAT scores, we can conduct a statistical analysis. Let's perform a t-test to compare the scores with the assumption that scores under normal conditions would average around 500. Here are the steps and results:

1. Calculate the mean of the verbal SAT scores.

Mean = (510 + 550 + 410 + 530 + 480 + 500 + 390 + 420 + 440) / 9 = 480.

2. Calculate the standard deviation of the scores.

Standard deviation = √[((510-480)² + (550-480)² + ... + (440-480)²) / (9-1)] ≈ 58.31.

3. Compute the t-value using the formula:

t = (mean - hypothetical mean) / (standard deviation / √n)

t = (480 - 500) / (58.31 / √9) ≈ -1.87.

4. Determine the degrees of freedom (df) which is n-1. In this case, df = 9 - 1 = 8.

5. Look up the p-value associated with the t-value and df in a t-table or use statistical software.

For t = -1.87 and df = 8, the p-value is approximately 0.1.

6. Finally, compare the p-value (0.1) to the significance level (0.05) to make a conclusion.

Since 0.1 > 0.05, we do not have enough evidence to conclude that the adverse conditions made a significant difference at the 0.05 level.

Step-by-step explanation: