Blue Green Grey Brown
UV 0 23 27 19 33
UV 1 35 16 20 20
UV 2 30 26 15 23
UV 3 54 23 21 15

data set contains the results of scientific tests performed on a sample of 400 inhabitants of Transylvania, who were selected at random from the population of that region. Eye colour was classified as follows: blue; green; grey; brown. Reaction to controlled exposure of ultraviolet light at a given fixed intensity was classified as follows:

uv0 = mild reaction;
uv1 = moderate reaction;
uv2 = severe reaction;
uv3 = extremely severe reaction.

Consider the following pair of hypotheses:

  • H0: ultraviolet light sensitivity is independent of eye colour ;
  • H1: ultraviolet light sensitivity is not independent of eye colour .

Using a suitable hypothesis test - based on the above hypotheses, and performed at the 5% significance level - on your individual dataset, investigate the independence of the eye colour of a Transylvanian and their reaction to ultraviolet light.
Your answers to parts (a),(b) and (c) should be given correct to three decimal place
  • (a). Enter the critical value:
  • (b). Enter the expected frequency (under the assumption that the null hypothesis is true) for the cell (UV0,Brown):
  • (c). Enter the value of the test statistic:
  • (d). Select the hypothesis test decision, based on your answers to parts (a) and (c): reject or dont reject H0?