Question

Math SAT Scores (Raw Data, Software Required):
Suppose the national mean SAT score in mathematics is 520. The scores from a random sample of 40 graduates from Stevens High are given in the table below. Use this data to test the claim that the mean SAT score for all Stevens High graduates is the same as the national average. Test this claim at the 0.10 significance level

(a) What type of test is this? This is a left-tailed test.This is a two-tailed test.    This is a right-tailed test. (b) What is the test statistic? Round your answer to 2 decimal places. tx=   (c) Use software to get the P-value of the test statistic. Round to 4 decimal places. P-value =   (d) What is the conclusion regarding the null hypothesis? reject H0 fail to reject H0    (e) Choose the appropriate concluding statement. There is enough data to justify rejection of the claim that the mean math SAT score for Stevens High graduates is the same as the national average. There is not enough data to justify rejection of the claim that the mean math SAT score for Stevens High graduates is the same as the national average.     We have proven that the mean math SAT score for Stevens High graduates is the same as the national average.

DATA ( n =40 ) MATH SAT Scores    504 523 542 506 454 412 513 487 473 546 461 510 529 430 561 461 520 514 586 555 549 516 485 524 563 504 506 526 548 563 512 513 513 510 519 546 558 448 577 492

Answer 1

Let X be the MATH SAT score        
         
n = 40                Sample Size     
x̅ = 513.975      Sample Mean     
s = 39.466          Sample Standard Deviation     
μ = 520               Population Mean     
α = 0.1               10% level of significance     
         
a) Since we have to test the claim that the mean SAT score for all Stevens High         
graduates is the same as the national average        
This is a two-tailed test        
         
b) Test statistic t is given by         
         
                
tx = -0.97        
         
c) df = Degrees of freedom = n - 1 = 40 -1 = 39        
We find the p-value using Excel function T.DIST.2T        (Since this is a 2 tailed test)
p-value = T.DIST.2T(0.97, 39)        ... (We use positive t value for the function)
p-value = 0.3380        
         
d) Since 0.3380 > 0.1        
that is p-value > α        
Hence we do not reject Ho        
Conclusion :        
Fail to reject Ho        
         
e) Concluding statatement        
There is not enough data to justify rejection of the claim that the mean math SAT score         
for Stevens High graduates is the same as the national average.