The table shows the amounts of caffeine (in milligrams) in 16-ounce servings for a random sample of beverages. At \(\alpha=0.01\), can you conclude that the distribution of the amounts of caffeine in at least one beverage is different from the others?

(a) identify the claim and state \(H_{0}\) and \(H_{a}\),

(b) find the critical value and identify the rejection region,

(c) find the test statistic \(H,\) 

(d) decide whether to reject or fail to reject the null hypothesis,

(e) interpret the decision in the context of the original claim.

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Beverage Amount of caffeine in 16-ounce serving (in milligrams) Coffees 320 300 206 150 266 Soft drinks 95 96 56 51 71 72 47 Energy drinks 200 141 160 152 154 166 Teas 100 106 42 15 32 10