Problem 2. (5 points) Trying to quit ~ NicotineLess Inc. manufactures Lo Nic, a special brand of cigarettes with a lower nicotine content. They market Lo Nic cigarettes to smokers who wish to quit smoking but are finding it difficult. The manufacturer claims that the amount of nicotine delivered to the body from smoking a Lo Nic cigarette is normally distributed with a mean of / = 409 mcg and a standard deviation o = 32.1 mcg. Yamamoto wants to quit smoking and is willing to try Lo Nic cigarettes, but he is suspicious and plans to investigate the advertised claim. He decides to test the hypotheses: Ho : / = 409 vs. Ha : H > 409 To conduct his test, Yamamoto will measure the amount of nicotine delivered to the body from a random sample of 12 Lo Nic cigarettes. If the sample mean is more than 421.8 mcg, he will file a complaint against NicotineLess Inc. for false advertising Round all calculated values to 4 decimal places. 1. Which of the following describes a Type I error in this situation? O A. Yamamoto does not file the complaint when the mean nicotine content is actually greater than 409 mg. O B. Yamamoto files the complaint when the mean nicotine content is actually not greater than 409 mg. O C. Yamamoto files the complaint when the mean nicotine content is actually greater than 409 mg. O D. Yamamoto does not file the complaint when the mean nicotine content is actually not greater than 409 mg. 2. Which of the following describes a Type II error in this situation? A. Yamamoto files the complaint when the mean nicotine content is actually not greater than 409 mg. O B. Yamamoto does not file the complaint when the mean nicotine content is actually not greater than 409 mg. O C. Yamamoto files the complaint when the mean nicotine content is actually greater than 409 mg. O D. Yamamoto does not file the complaint when the mean nicotine content is actually greater than 409 mg 3. What is the probability that Yamamoto will make a Type I error with this decision rule? Probability of a Type I error = 4. Using the decision rule, what is the power of the hypothesis test if the mean nicotine content in Lo Nic cigarettes is actually 428.3 mcg? Power = 5. Yamamoto reconsiders his decision rule and decides to file the complaint if the mean nicotine content in the sample of 12 cigarettes is more than 428.9 mcg instead of 421.8 mcg. What will happen to the Type I error rate if he makes this change? Will the change cause the Type I error rate to increase, decrease, or stay the same? O A. Increase O B. Decrease O C. Stay the same Note: You can earn partial credit on this
