Question

Carlos conducts a study comparing the performance of individuals on the first quiz in each of two classes taken in the first term of their freshman year. The scores, out of 100, are provided for nine individuals in both classes. Class 1: 87, 78, 87, 85, 93, 98, 83, 82, and 73 Class 2: 87, 86, 92, 90, 90, 91, 89, 78, and 76 The value for t is _____. (Answer using 2 decimal places.)

Answer 1

-0.46

Explanation:

We have small sample sizes n1 = 9 and n2 = 9.
`\bar{x}_(1) = 85.11`,
`\bar{x}_(2) = 86.56`;
`s_(1) = 7.47`,
`s_(2) = 5.75`.

`s_(p)^(2) = ((n_(1)-1)s_(1)^(2)+(n_(2)-1)s_(2)^(2))/(n_(1)+n_(2)-2) = ((9-1)(7.47)^(2)+(9-1)(5.75)^(2))/(9+9-2) = 44.43`

Because Carlos conducts a study comparing the performance of individuals on the first quiz in each of two classes taken in the first term of their freshman year, the hypothesis null is
`H_(0): \mu_(1)-\mu_(2) = 0`, then, the observed t-value is

`t=\frac{(\bar{x}_(1)-\bar{x}_(2))-0}{s{p}√(1/n1+1/n2)} = (-1.45)/(6.67(0.47)) =  -0.46`