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 LaTeX: / sigma = 100σ = 100. Is the principal's claim valid? Use a level of significance of LaTeX: / alpha = 0.05α = 0.05.

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Caitlyn

Mathematics

18 March, 18:47

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 LaTeX: / sigma = 100σ = 100. Is the principal's claim valid? Use a level of significance of LaTeX: / alpha = 0.05α = 0.05.

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Cloe Parker · Answer 1

z = (574-550) / (100/sqrt (72)) = 2.036

p-value = 0.0209

Reject the null hypothesis. There is sufficient evidence to suggest that the students' mean SAT score is greater than 550. The principal was right.