A study has been made to compare the nicotine contents of two brands of cigarettes. 5 cigarettes of Brand A had an average nicotine content of 4.3 milligrams with a standard deviation of 0.5 milligram, while eight cigarettes of Brand B had an average nicotine content of 2.7 milligrams with a standard deviation of 0.7 milligram. Assuming that the two sets of data are independent random samples from normal popuiations with equal variances, construct a 95% confidence interval for the difference between the mean nicotine contents of the two brands of cigarettes.
A study has been made to compare the nicotine contents of two brands of cigarettes. 5 cigarettes of Brand A had an average nicotine content of 4.3 milligrams with a standard deviation of 0.5 milligram, while eight cigarettes of Brand B had an average nicotine content of 2.7 milligrams with a standard deviation of 0.7 milligram. Assuming that the two sets of data are independent random samples from normal popuiations with equal variances, construct a 95% confidence interval for the difference between the mean nicotine contents of the two brands of cigarettes.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:**Comparison of Nicotine Contents in Cigarettes: A Statistical Approach**
In a recent study, researchers aimed to compare the nicotine contents of two different brands of cigarettes. They examined the following data:
- **Brand A**: Five cigarettes were tested, revealing an average nicotine content of 4.3 milligrams with a standard deviation of 0.5 milligrams.
- **Brand B**: Eight cigarettes were tested, showing an average nicotine content of 2.7 milligrams with a standard deviation of 0.7 milligrams.
The objective was to determine a 95% confidence interval for the difference in mean nicotine contents between the two brands. The study assumes the following:
- The data sets for each brand are independent random samples.
- The populations are normally distributed with equal variances.
This analysis helps in understanding if there is a significant difference in nicotine content between the two brands of cigarettes.
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