The national mean SAT score in math is 550. Suppose a high school principal claims that the mean SAT score in math at his school is better than the national mean score. A random sample of 72 students finds a mean score of 574. Assume that the population standard deviation is sigma=100. Is the principal's claim valid? Use a level of significance of alpha=0.05.

Compute the test statistic for this analysis. Round your answer to 3 decimal places.
Z=
Determine the P-value based the test statistic. Round your answer to 3 decimal places.
P-value=
State your decision based on the P-value and the level of significance (alpha) and give your conclusion in an English sentence.
-Reject the null hypothesis. There is insufficient evidence to suggest that the students' mean SAT score is greater than 550. The principal was right.
-Reject the null hypothesis. There is sufficient evidence to suggest that the students' mean SAT score is greater than 550. The principal was right.
-Fail to reject the null hypothesis. There is insufficient evidence to suggest that the students' mean SAT score is greater than 550. The principal was wrong.
-Fail to reject the null hypothesis. There is sufficient evidence to suggest that the students' mean SAT score is greater than 550. The principal was wrong.