Chi-Square Goodness-of-Fit Test

Problem 1

It is suggested that dispersal of seeds from the edge of a plantation of trees follows an inverse square law (i.e. the number of seeds travelling x m is proportional to l/x2 ). We want to test this theory using an isolated stand of trees on an area of moorland. Seeds will be collected in four 0.25 m 2 plots at each of five distances, on the downwind side of the plantation.

Distance (m)	5	10	15	25	50
Seeds (observed)	200	65	14	12	3
Seeds (expected)	208.4	52.1	23.1	8.3	2.1

1. State the hypotheses (H₀& H_a).

2. Perform calculation in Minitab or SPSS.

3. Screen capture of the process and results in Minitab or SPSS.

4. Interpret results.

5. State the appropriate conclusion.

Problem 2

It has been known for a long time that sickle cell anemia, a mutation in the gene controlling one of the proteins that make up haemoglobin in humans, is more common in areas where malaria is endemic. The sickle cell trait is recessive but, although it is not fully understood why, heterozygous individuals are known to have some protection against the symptoms of malaria. This advantage is sufficient to maintain the sickle cell alleles in such populations, even though the homozygotes suffer from the debilitating disease sickle cell anemia. Because the heterozygotes can be recognized from a blood test, it is possible to establish at what frequency sickle cell alleles exist in a population.

A recently collected sample of blood tests from 886 randomly chosen individuals in Gabon contained the following genotypes:

Phenotype	Observed frequency	Expected frequency
Normal/Normal (A/A)	700	705.26
Normal/Sickle (A/S)	180	170.11
Sickle/Sickle (S/S)	6	10.63

1. State the hypotheses (H₀& H_a).

2. Perform calculation in Minitab or SPSS.

3. Screen capture of the process and results in Minitab or SPSS.

4. Interpret results.

5. State the appropriate conclusion.