5. Caffeine in Tea Bags In a recent study, researchers found that the average amount of caffeine in tea bags is 26 mg. The standard deviation of the population is 3 mg. If a random sample of 32 newly manufactured tea bags has a mean of 24.8 mg of caffeine, can it be concluded that the new brand of tea bags contain less caffeine than the average found in the recent study? Use ? = 0.10.
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- Null hypothesis (\(H_0\)): The mean caffeine content of the new tea bags is equal to 26 mg (\(\mu = 26\)). - Alternative hypothesis (\(H_a\)): The mean caffeine content of the new tea bags is less than 26 mg (\(\mu < 26\)). Show more…
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Caffeine in Tea Bags In a recent study, researchers found that the average amount of caffeine in tea bags is 26 mg. The standard deviation of the population is 3 mg. If a random sample of 33 newly manufactured tea bags has a mean of 26.1 mg of caffeine, can it be concluded that the new brand of tea bags contain greater caffeine than the average found in the recent study? Use a = 0.05, and use the P-value method with tables. (c) Find the P-value. Round the answer to at least four decimal places.
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Suppose the coffee industry claimed that the average adult drinks 1.8 cups of coffee per day: To test this claim, a random sample of 40 adults was selected, and their average coffee consumption was found to be 1.85 cups per day: Assume the standard deviation of daily coffee consumption per day is 0.5 cups. Using a = 0.05, complete parts a and b below: a. Is the coffee industry's claim supported by this sample? Determine the null and alternative hypotheses: H0: μ = 1.8 H1: μ ≠ 1.8
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