Question

1. All cigarettes presently on the market have a mean nicotine content of 1.6 mg per cigarette. A firm that produces cigarettes claims that it has discovered a new way to cure tobacco leaves that will result in the mean nicotine per cigarette being less than 1.6 mg. To test this claim, a sample of 36 of the firm's cigarettes were analyzed. Assume that the standard deviation of the cigarettes nicotine content is 0.8 mg. (a) (5 points) What conclusions can be drawn, at the 5% level, if the average nicotine content of the 36 cigarettes is 1.54 mg? (b) (5 points) If the truth is 1.5 mg per cigarette, what is the minimum sample size to have at least 90% power to detect it for such 5% level significance test?

          1. All cigarettes presently on the market have a mean nicotine content of 1.6 mg per cigarette. A firm that produces cigarettes claims that it has discovered a new way to cure tobacco leaves that will result in the mean nicotine per cigarette being less than 1.6 mg. To test this claim, a sample of 36 of the firm's cigarettes were analyzed. Assume that the standard deviation of the cigarettes nicotine content is 0.8 mg.
(a) (5 points) What conclusions can be drawn, at the 5% level, if the average nicotine content of the 36 cigarettes is 1.54 mg?
(b) (5 points) If the truth is 1.5 mg per cigarette, what is the minimum sample size to have at least 90% power to detect it for such 5% level significance test?

1. All cigarettes presently on the market have a mean nicotine content of 1.6 mg per cigarette. A firm that produces cigarettes claims that it has discovered a new way to cure tobacco leaves that will result in the mean nicotine per cigarette being less than 1.6 mg. To test this claim, a sample of 36 of the firm's cigarettes were analyzed. Assume that the standard deviation of the cigarettes nicotine content is 0.8 mg.
(a) (5 points) What conclusions can be drawn, at the 5% level, if the average nicotine content of the 36 cigarettes is 1.54 mg?
(b) (5 points) If the truth is 1.5 mg per cigarette, what is the minimum sample size to have at least 90% power to detect it for such 5% level significance test?

Added by Jody B.

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