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.29
(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 in part (a)?

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Cat Before (Y) After (5) Difference Amelia Bathsheba Boris Frank Jupiter Lupine Madonna Michelangelo Oregano Phantomm Posh Sawver Scary Slater Tucker Mean SD 0. 1.8 1.66 2.8 1.20