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Snow Geese lay 4 eggs in a nest. A field biologist wanted to know if there...

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Statistics

Snow Geese lay 4 eggs in a nest. A field biologist wanted toknow if there is a relationship between the order in which the eggsare laid and the sex of each egg. Please see the table below.

Egg order ->1234Total
Male17167545
Female109171450
Total2725241995

Is there a relationship between sex and laying order insnow geese?

1. What are the null and alternate hypotheses for the chi-squaregoodness of fit test?

2. What are the expected counts under the null hypothesis?

3. Use Minitab to determine a chi-square test statistic and Pvalue

4. Do you accept or reject the null?

Answer & Explanation Solved by verified expert
3.6 Ratings (642 Votes)

a)

Ho: there is no relationship between two given two variables

Ha: there is a relationship between two given two variables

b)

Chi-Square Test of independence Observed Frequencies
0
0 1 2 3 4 Total
male 17 16 7 5 45
female 10 9 17 14 50
Total 27 25 24 19 95
Expected frequency of a cell = sum of row*sum of column / total sum
Expected Frequencies
1 2 3 4 Total
male 27*45/95=12.789 25*45/95=11.842 24*45/95=11.368 19*45/95=9 45
female 27*50/95=14.211 25*50/95=13.158 24*50/95=12.632 19*50/95=10 50
Total 27 25 24 19 95
(fo-fe)^2/fe
male 1.3862 1.4599 1.679 1.778
female 1.2476 1.3139 1.511 1.600

c)

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   11.9747
  Number of Rows =   2
Number of Columns =   4
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 4- 1 ) =   3
  
p-Value =   0.0074705

d)

Decision:    p-value < α , Reject Ho  

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