Most fish use gills for respiration in water and researchers can observe how fast a fish’s gill cover beats to study ventilation, much like we might observe breathing rate for a person. Professor Brad Baldwin is interested in how water chemistry might affect gill beat rates. In one experiment he randomly assigned fish to tanks with different levels of calcium. One tank was low in calcium (0.71 mg/L), the second tank had a medium amount (5.24 mg/L), and the third tank had water with a high calcium level (18.24 mg/L). His research team counted gill rates (beats per minute) for samples of 30 fish in each tank. The results are stored in FishGills3. (Note: You may also see a file called FishGills12 which is a more extensive experiment with 12 tanks.)

(a) Use technology to check that the conditions for an ANOVA model are reasonable for these data. Include a plot that compares the gill rates for the three calcium conditions.

(b) If the conditions are met, use technology to find the ANOVA table and complete the test. If the conditions are not reasonable, use a randomization test (scrambling the calcium levels) to complete the test.