Question

18. Scores this year on the SAT mathematics test (SAT-M) for students taking the test for the first time are believed to be Normally distributed with mean 4. For students taking the test for the second time, this year's scores are also believed to be Normally distributed but with a possibly different mean 42. We wish to estimate the difference - A random sample of the SAT-M scores of 100 students who took the test for the first time this year was obtained, and the mean of these 100 scores was 11 = 504.5, while the standard deviation was 01 = 100. A random sample of the SAT-M scores of 30 students who took the test for the second time this year was also obtained, and the mean of these 30 scores was 13 = 539.1 while the standard deviation was 02 = 90. A 95% confidence interval for My - 11 is:

Answer 1

Given that ne 100 ne=30 X 504.5 M2= 539.) 5,= 100, J2=90 for ast of confidence, zx12=1.96. SE = Standard erra n2 = 19.2354 E The Margin of corror The 95%. Confidence 2x12(SE) = 37.7014 Internal for she is Crén-12-E, &,-K2+) (504.5-539..- 37-7014,504.5-539.1+37.7014 (-72.3014, 3.1014).