Question

An ornithologist has 4 bird feeders at separate locations. She wonders if birds are equally likely to visit each of the feeders. She recorded data for a sample of 300 recent visits. Here are the results:

Feeder 1 2 3 4
Observed visits 60 90 92 58
A test is performed to determine if these results suggest that birds visit one specific feeder more often than the other feeders. What is the xa test statistic?
a. 13.71
b. 0
c. 14.37
d. 3
e. 1028

Answer 1

the x² test statistic 13.71

Option a) 13.71 is the correct answer.

Explanation:

Given the data in the question;

Feeder 1 2 3 4

Observed visits;
`o_i` 60 90 92 58

data sample = 300

Expected
`e_i` = 300 / 4 = 75

the x² test statistic = ?

`X^2_{stat` = ∑[ (
`o_i` -
`e_i`)²/
`e_i`]

`X^2_{stat` = [ (60 - 75)² / 75 ] + [ (90 - 75)² / 75 ] + [ (92 - 75)² / 75 ] + [ (58 - 75)² / 75 ]

`X^2_{stat` = [ 3 ] + [ 3 ] + [ 3.8533 ] + [ 3.8533 ]

`X^2_{stat` = 13.7066 ≈ 13.71

Therefore, the x² test statistic 13.71

Option a) 13.71 is the correct answer.