A random sample of 60 mathematics majors spent an average of $200.00 for textbooks for a term, with a standard deviation of $22.50. A random sample of 40 English majors spent an average of $180.00 for textbooks that term, with a standard deviation of $18.30. Calculate a 90% pooled confidence interval for the difference in average amounts spent on textbooks (math majors - English majors).
A) (12.91, 27.09)
B) (11.50, 28.50)
C) (13.19, 26.81)
D) None of the above

Question

Quizplus · Accepted Answer

The correct answer is A.The pooled standard deviation is:s_p = sqrt(((n1-1)*s1^2 + (n2-1)*s2^2) / (n1+n2-2))= sqrt(((60-1)*22.50^2 + (40-1)*18.30^2) / (60+40-2))= 20.41The 90% pooled confidence interval for the difference in average amounts spent on textbooks is:(x1 - x2) +/- z*sqrt(s_p^2/n1 + s_p^2/n2)= (200.00 - 180.00) +/- 1.645*sqrt(20.41^2/60 + 20.41^2/40)= (20.00) +/- 17.00= (12.91, 27.09)

A Random Sample of 60 Mathematics Majors Spent an Average