Problem 6BSC

use the Kruskal - Wallis test.

Clancy, Rowling, Tolstoy Readability Pages were randomly selected by the author from The Bear and the Dragon by Tom Clancy, Harry Potter and the Sorcerer’s Stone by J. K. Rowling, and War and Peace by Leo Tolstoy. The Flesch Reading Ease scores are listed on the next page. Use a 0.05 significance level to test die claim that the three samples are from populations with the same median. Do the books appear to have different reading levels of difficulty?

Clancy 58.2 73.4 73.1 64.4 72.7 89.2 43.9 76.3 76.4 78.9 69.4 72.9

Rowling 85.3 84.3 79.5 82.5 80.2 84.6 79.2 70.9 78.6 86.2 74.0 83.7

Tolstoy 69.4 64.2 71.4 71.6 68.5 51.9 72.2 74.4 52.8 58.4 65.4 73.6

Solution 6BSC

The value of the test statics is,

Since each sample has 12 observations, the distribution of H is approximately a chi-square distribution with k -1 degrees of freedom. The number of samples is k = 3, thus there are 2 degrees of freedom for H.

Now from the table A-4 the critical value is found corresponding to 2 degrees of freedom at 0.05 level of significance as 5.991. As the value of the test statistic falls in the critical region as seen from the figure.