Question

The U.S. Department of Agriculture claims that the mean annual consumption of tea by a person in the United States is 8.9 gallons. A random sample of 60 people in the United States has a mean annual tea consumption of 8.2 gallons. Assume the population standard deviation is 2.2 gallons. At a=0.10, can you reject the claim?

Answer 1

To determine if we can reject the claim made by the U.S. Department of Agriculture regarding the mean annual consumption of tea, we can conduct a hypothesis test using a z-test.

Step-by-step explanation:

To determine if we can reject the claim made by the U.S. Department of Agriculture, we need to conduct a hypothesis test. Since we have a sample mean, sample size, and population standard deviation, we can use a z-test.

First, we state the null and alternative hypotheses. The null hypothesis is that the mean annual consumption of tea is 8.9 gallons, while the alternative hypothesis is that it is less than 8.9 gallons.

Next, we determine the test statistic by calculating the z-score using the formula: z = (sample mean - population mean) / (population standard deviation / sqrt(sample size)).

Finally, we compare the z-score to the critical value at a significance level of 0.10. If the z-score is less than the critical value, we can reject the null hypothesis and conclude that the mean annual consumption of tea is less than 8.9 gallons.