SOLUTION: 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 sa

Question 1109276: 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 σ=100. Is the principal's claim valid? Use a level of significance of α=0.05.
A) Compute the test statistic for this analysis. Round your answer to 3 decimal places.
B) Determine the P-value based on the test statistic. Round your answer to 3 decimal places.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Two way test to see if any different (one may argue in favor of a one way test, but this question sounds more like hoping it was better rather than knowing a priori it would be.)
usual assumptions or normality
z=test with critical value |z|>1.96
z=(xbar-mean)/sigma/sqrt(n)
z=24*sqrt(72)/100, inverting the denominator to multiply
z=2.036, the test statisitic
This has a p-value of 0.041, and is considered significant at the 0.05 level and supports the principal's claim.
RELATED QUESTIONS
The average math SAT score is 513 with a standard deviation of 113. A particular high... (answered by stanbon)

The average math SAT score is 518 with a standard deviation of 115. A particular high... (answered by stanbon)

the average Math SAT score is 513 with a standard deviation of 119 a particular high... (answered by Boreal)

The average math SAT score is 516 with a standard deviation of 117. A particular high... (answered by ewatrrr)

The average math SAT score is 511 with a standard deviation of 199. A particular high... (answered by Boreal)

The College Board reports that the nationwide mean SAT Math score was 515 in 2007. Assume (answered by stanbon)

Could someone please help with this?: The SAT math scores for all seniors in a high... (answered by ewatrrr)

Trevor wants to buy a local restaurant. 60% of the business days it's open, the... (answered by stanbon)

The problem is For a given population of high school seniors , the Scholastic Aptitude... (answered by stanbon)