1. (A) Caffeine Content: A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.7 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty-six 12-ounce bottles of caffeinated soft drinks has a mean caffeine content of 36.4 milligrams. Assume the population standard deviation is 10.8 milligrams. Answer the following questions:

What are the null and alternate hypothesis? How do you know? Which one is the claim, why?

Is this a left-tailed, right tailed, or two-tailed test? How do you know?

(B)Caffeine Content: A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.7 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty-six 12-ounce bottles of caffeinated soft drinks has a mean caffeine content of 36.4 milligrams. Assume the population standard deviation is 10.8 milligrams. Answer the following questions:

What is the test statistic? Is it a z or t value? Why?

What is the P-Value? How do you know?

If the level of significance is 0.05, will we reject or fail to reject the null hypothesis? Why?

What conclusion can we draw about the claim?

(C)Used Car Cost: A used car dealer says that the mean price of a three-year-old sport utility vehicle (in good condition) is $20,000. You suspect this claim is incorrect and find that a random sample of 22 similar vehicles has a mean price of $20,640 and a standard deviation of $1990. Answer these questions:

Will we use the z-or t-distribution for this test? Why?

What are the null and alternate hypothesis? How do you know? Which one is the claim, why?

Is this a left-tailed, right tailed, or two-tailed test? How do you know?