A comparison of the amount of nicotine that could be inhaled from cigarettes of the same brand differs between countries. There is some suspicion that local cigarette companies boosted their cigarettes' nicotine content to maintain or increase present addictive levels. A study of 40 randomly chosen cigarettes was conducted to investigate this issue between two European countries. The recorded average level of nicotine content in cigarettes in both countries is given below: Country A: 0.85 mg/cigarette with a standard deviation of 0.2 mg/cigarette. Country B: 1.30 mg/cigarette with a standard deviation of 0.18 mg/cigarette. Does the nicotine content in the two countries differ? Test at the 5% level of significance.
Added by Yolanda S.
Step 1
85 mg/cigarette - Standard deviation (S1) = 0.2 mg/cigarette - Country B (Population 2): - Sample size (n2) = 40 - Mean nicotine content (X2) = 1.30 mg/cigarette - Standard deviation (S2) = 0.18 mg/cigarette ** Show more…
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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?
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