Question

An ecologist counted the number of eggs in randomly selected nests in a population of birds. To test the hypothesis that the number of eggs per nest follows a Poisson distribution at the 5% level of significance, you will need to compare a calculated value with a critical value.

Eggs Number of nests Prob Expected
nest, xi per fi
0 15 0.2845 19.9
1 29 0.3576 25.0
2 19 0.2248 15.7
23 7 0.1331 9.3
SUM: 70 1.0000 70.0
What are the calculated and critical values for this test?
a. calculated = 45.6; critical = 5.991.
b. calculated = 3.10; critical = 5.991.
c. calculated = 5.89; critical = 5.991.
d. calculated = 3.10; critical = 7.815.

Answer 1

d. calculated = 3.10; critical = 7.815.

Step-by-step explanation:

To test the hypothesis Given in the question above, we use the Chisquare goodness of fit :

The test statistic is defined as :

χ² = Σ(Observed - Expected)² / Expected

Observed = number of nests

χ² = ((15 - 19.9)^2 / 19.9) + ((29 - 25)^2 / 25) + ((19 - 15.7)^2 / 15.7) + ((7 - 9.3)^2 / 9.3)

χ² = 3.1089

The critical value :

df = n - 1 = 4 - 1 = 3

The critical value ;P(χ² at 0.05, df = 3 ) = 7.815