A quality-control manager wants to test whether there is any difference in the median length of life of light bulbs between three different brands. Random samples were drawn from each brand where the duration of each light bulb (in hours) was measured. The results are shown in the accompanying table.

Brand 1..................... Brand 2.................... Brand 3

375................................. 280......................... 350

400................................. 290......................... 415

425................................. 300......................... 425

410................................. 325......................... 380

420................................. 350......................... 405

a. Specify the competing hypotheses to test whether some differences exist in the median length of life of light bulbs between the three brands.

b. Calculate the value of the test statistic H.

c. Approximate the p-value.

d. At the 10% significance level, do some differences exist between the median length of life of light bulbs by brand? Explain.