In a discussion of SAT scores, someone comments\"because only a minority of high
ID: 3156631 • Letter: I
Question
In a discussion of SAT scores, someone comments"because only a minority of high school students take the test, the scores overestimates the ability of typical high school seniors. The mean Sat mathematics score is about 475, but I think that if all seniors took the test , the mean score would be no more than 450". You have the test to a random sample of 500 seniors from California. These students had a mean scores of sample mean=461. The population standard deviation is 100. Is this good evidence against the claim that the mean for all California seniors is not more than 450? Use alpha=0.05. Show all the formulas ,Ho Ha , z statistic, p value and the conclusion in the context of the hypothesis.
Explanation / Answer
N = 500 THEREFORE THREATED A NOMRAL
THE NULL HYPOTHESIS = H0= u = 475
the alternate hypothesis = Ha= u<475
the alpha = 0.05
therefore from the left tail test and from the z table
the critical value = z<-1.96
z stats = (461-475)/(100/sqrt(500) = -3.13
as the z = -3.13
the pvalue = 0.0009