Conclusions in a goodness-of-fit test

When Silvia feeds her cat, she places food in

3

different locations. She wondered if her cat was equally likely to eat first from each of the locations, so she tallied which location her cat chose first in a sample of

30

feedings. Here are the results along with a chi-square goodness-of-fit test:

Location	Kitchen	Bedroom	Living room
Hypothesized	$0.333$ ‍	$0.333$ ‍	$0.333$ ‍
Observed	$13$ ‍	$13$ ‍	$4$ ‍
Expected	$10$ ‍	$10$ ‍	$10$ ‍
Components	$0.9$ ‍	$0.9$ ‍	$3.6$ ‍
$χ^{2} = 5.4, DF = 2$ ‍
$P-value = 0.067$ ‍

Assume that all conditions for inference were met.

At the $α = 0.05$ ‍ significance level, what should Silvia conclude about her cat's feeding preferences?

(Choice A)
There is sufficient evidence to conclude that her cat prefers to eat first from some locations more than others.
(Choice B)
There's not enough evidence to conclude that her cat prefers to eat first from some locations more than others.
(Choice C)
There is sufficient evidence to conclude that her cat is equally likely to eat first from each of the locations.
(Choice D)
No conclusions can be made from this test, because one of the observed counts is too low for the calculations to be accurate.

AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 12

Problem