An urn contains a very large number of marbles of four different colors: red, orange, yellow, and green. A sample of 12 marbles drawn at random from the urn revealed 2 red, 5 orange, 4 yellow, and 1 green marble. Test the hypothesis that the urn contains equal proportions of the differently colored marbles at 0.05 level of significance. We cannot reject the hypothesis at the 0.05 significance level.

We can reject the hypothesis at the 0.05 significance level.

Step-by-step explanation:

given that an urn contains a very large number of marbles of four different colors: red, orange, yellow, and green. A sample of 12 marbles drawn at random from the urn revealed 2 red, 5 orange, 4 yellow, and 1 green marble.

H0: All colours are equally likely

Ha: atleast two colours are not equally likely

(Two tailed chi square test at 5% significance level)

color Red Orange Yellow Green total

Observed O 2 5 4 1 12

Expected E 3 3 3 3 12

(O-E) ^2/E 0.3333 5.3333 0.3333 5.3333 11.3333

chi square = 11.3333

df = 3

p value = 0.010055

Since p < 0.05 we reject H0

We can reject the hypothesis at the 0.05 significance level.