Question

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

Egg order ->	1	2	3	4	Total
Male	17	16	7	5	45
Female	10	9	17	14	50
Total	27	25	24	19	95

Is there a relationship between sex and laying order in snow geese?

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

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

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

4. Do you accept or reject the null?

Answer 1

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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