Answer:
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: