Question

Five colors of floor tiles are to be laid in a random pattern (that is, the frequency of each color is to be the same. A sample of 100 tiles laid exactly as they were packaged was observed and the following was found Color White Red Green Yellow Purple No. of Tiles 16 18 24 25 17 Test the hypothesis at the 5 percent level of significance that the color distribution is uniform

Answer 1

Let the null hypothesis H_o be the frequencies of each color is to be same Given that Therefore the expected frequency sigma = 100/5 = 20 \r\n calculation of x^2 = Sigma(O_i - E_i)^2/E_i x^2 = 3.5 the table value of lambda^2 with v = n - 1 = 5 - 1 = 4 degrees of freedom at 5% level of significance x^2_0.05 = 9.488 since calculated value of lambda^2 < table value of x^2, i.e, 3.5 < 9.488 we accept the null hypothesis H_0 and conclude that the frequencies of each color is to be same.