Statistics help?

Question

Can anyone help with this qn?

Over a specified period, observers sighted 200 birds at a particular location. The birds were
classified into four species as shown in the table below. The previously known proportion of
species for that location was 3:3:3:1.
Species 1 2 3 4 Total
No. of birds 46 74 65 15 200
(Source: P.V. Rao (1998), Statistical Research Methods in the Life Sciences, Duxbury
(a) Calculate the expected number of birds for each species, assuming that the composition
of species has not changed.
(b) Is there evidence to suggest that the composition of the species in that location has
changed? Conduct the appropriate test.
(c) With reference to the observed and expected values write an informative conclusion.

Answer 1

the expected values are found by looking at the ratio 3:3:3:1

there are ten parts, 30% species 1, 30% species 2, 30% species 3 and 10% species 4.

the expected values are thus
60, 60, 60, 20

the chi square statistic is:
1/200 * ( (46 -60)² + (74 - 60)² + (65 - 60)² + (15 - 20)²)
= 2.21

this chi-squared statistic has 3 degrees of freedom

the p-value is P(X > 2.21) ≈ 0.53

this is not enough evidence to reject the null hypothesis. the null hypothesis for this test is that the multinomial trial follows the expected proportions. This test says it is plausible that the species do follow the expected proportions.

Answer 2

Think "chi-squared". This is the common test for enumerative data such as you have here. If I remember right, for each species, you compute
absolute(actual-expected)^2/expected. Add the four computation and test it against the chi-square distribution with 3 degrees of freedom.