the average math SAT score is 517 with a standard deviation of 118. A particular high school claims that its students have unusually high math SAT scores. A random sample of 55 students from this school was selected, and the mean math SAT score was 561. Is the high school justified in its claim?

We need to find out whether 561 deviates significantly from the mean 517 to be considered exceptionally high. Work out the score (561-517)/118=0.3729 approximately. As a Z score this corresponds to 0.645, which means that 64.5% of SAT results would be below 561 and 35.5% would therefore be above 561. To be significant, we need only a small number of results to be higher than 561 (say, 5%) if we were to consider 561 to be exceptionally high. Even using the t-test with 55-1=54 degrees of freedom, we are nowhere near the critical value, so we can say with a reasonable degree of confidence that 561 is not significantly high enough to be considered exceptional, so the high school is not justified in its claim.

by Top Rated User (788k points)