A volunteer working at an animal shelter conducted a study of the effect of catnip on cats at the shelter. She recorded the number of "negative interactions" each of 15 cats made in 15-minute periods before and after being given a teaspoon of catnip. The paired measurements were collected on the same day within 30 minutes of one another; the data are given in the accompanying table.
(a) Construct a 95% confidence interval for the difference in mean number of negative interactions.
(b) Construct a 95% confidence interval the wrong way, using the independent-samples method. How does this interval differ from the one obtained part (a)?
|
CAT
|
BEFORE
( ri )
|
AFTER
( r2)
|
DIFFERENCE.
|
|
Amelia
|
0
|
0
|
0
|
|
Bat hsheba
|
3
|
6
|
-3
|
|
Boris
|
3
|
4
|
-I
|
|
Frank
|
0
|
1
|
-1
|
|
Jupiter
|
0
|
0
|
0
|
|
Lupine
|
4
|
5
|
-1
|
|
Madonna
|
1
|
3
|
-2
|
|
Michelangelo
|
2
|
1
|
1
|
|
Oregano
|
3
|
5
|
-2
|
|
Phantom
|
5
|
7
|
-2
|
|
Posh
|
1
|
0
|
1
|
|
Sawyer
|
0
|
1
|
- I
|
|
Scary
|
3
|
5
|
-2
|
|
Slater
|
0
|
2
|
-2
|
|
Tucker
|
2
|
2
|
0
|
|
Mean
|
1.8
|
2.8
|
- I
|
|
SD
|
1.66
|
2.37
|
1.20
|