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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

Sagot :

nuhulawal20

Answer:

the x² test statistic 13.71

Option a) 13.71 is the correct answer.

Step-by-step explanation:

Given the data in the question;

Feeder                     1      2      3       4

Observed visits; [tex]o_i[/tex]  60   90   92    58

data sample = 300

Expected [tex]e_i[/tex] = 300 / 4 = 75

the x² test statistic = ?

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

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

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

[tex]X^2_{stat[/tex] = 13.7066 ≈ 13.71

Therefore, the x² test statistic 13.71

Option a) 13.71 is the correct answer.

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