Question

A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. Construct a​ 95% confidence interval for the mean difference between the before and after scores. Is there evidence to suggest the logic course improves abstract reasoning? You may assume that the differences for the dependent samples are normally distributed.

Before 74, 83, 75, 88, 84, 63, 93, 84, 91, 77
After 73, 77, 70, 77, 74, 67, 95, 83, 84, 75
Note : define d = before - after, then đ = 3.7 and s = 4.95

Answer 1

The right answer is "
`0.2<\mu d<7.2`".

Explanation:

The given values are:

`\bar{x_0} = 3.7`

`s_o=4.95`

`t_{(0.05)/(2) }=2.2621`

As we know,

95% confidence for
`\mu_0` will be:

=
`\bar{x_0} \pm t_{(0.05)/(2) },n-1* (s_o)/(√(n) )`

The lower bound will be:

=
`3.7-2.2621* (4.95)/(√(10) )`

=
`0.16\simeq 0.2`

The upper bound will be:

=
`3.7+2.2621* (4.95)/(√(10) )`

=
`7.23\simeq7.2`

Thus the right answer is "
`0.2<\mu d<7.2`"