The following table shows age distribution and location of a random sample of 166 buffalo in a natio

pettingyg0

pettingyg0

Answered question

2022-04-22

The following table shows age distribution and location of a random sample of 166 buffalo in a national park.
 Age  Lamar District  Nez Perce District  Firehole District  Row Total  Calf 15161041 Yearling 12111033 Adult 35292892 Column Total 625648166
Use a chi-square test to determine if age distribution and location are independent at the 0.05 level of significance.
1. Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)
2. What are the degrees of freedom?

Answer & Explanation

Ciara Melton

Ciara Melton

Beginner2022-04-23Added 12 answers

The given information is about the age distribution and location of a random sample of 166 buffalo in a national park.
1. Chi-square test statistic:
χ2=(OiEi)2Ei
Calculate the expected frequencies are as follows:
 Age  Lamar District  Nez Perce District  Firehole District  Total  Calf 41×62166=15.313341×56166=13.831341×48166=11.855441 Yearling 33×62166=12.325333×56166=11.132533×48166=9.542233 Adult 92×62166=34.361492×56166=31.036292×48166=26.602492 Total 625648166
Calculate the chi-square test statistic is as follows:
χ2=(1515.3133)215.3133+(1613.8313)213.8313+(1011.8554)211.8554+(1212.3253)212.3253+(1111.1325)211.1325
+(109.5422)29.5422+(3534.3614)234.3614+(2931.0362)231.0362+(2826.6024)226.6024=
=0.0064+0.3400+0.2904+0.0086+0.0016+0.0220+0.0119+0.1336+0.0734
=0.88790.888
Therefore, the value of the chi-square test statistic is 0.888.
Degrees of freedom:
Calculate the degrees of freedom is as follows:
df=(r1)(c1)=(31)(31)=4
Therefore, the degrees of freedom is 4.
Answer:
1. The value of the chi-square test statistic is 0.888.
2. The degrees of freedom is 4.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?