Question

If a math department chair says that the average score for math is 60 out of 100 pts. Do you believe it? Show your work.

sample size 32 mean 64 15.82 Sample standard deviation population standard deviation 12.5 max 90 Q1 60 Median 69.5 Q3 75

Answer 1

Looking at the table , the mean score is 64 and the sample standard deviation is 15.82, for the sample of size 32.

So it's questionable to believe that the average score in Math is 60 out of 100, as the standard deviation is too high for 32 observations.

There is a very good way of checking it, by hypothesis testing.

S Let Xi = {th student's score in Math, i=1 (1) 32. Lot x; it (pes o2) i-com Here, the testing problem is? Ho : Je=po ag. Hi: Mello, with Mo= 60. Test statistic: T = rn (X-40) ~ tn... under Ho. Reject to at leveld, if obs | Iltal. obs. (T1 = a (-os) 2 (64-60) 1.43. tai noi toos; 32-1 obs17! <toint >> We accept Ho, at level 2-0-05 30, 4 believe that the average score for math is 60. 132 S 15.82 to.025; 31 = 2.039.

So it's believable with almost 95% confidence that the mean score is 60, out of 100.