A researcher is interested in whether the true concentration of
nicotine in cigarettes (in milligrams) is equal to the claimed
amount of 1mg. This researcher provides the following 95%
confidence interval for the amount of nicotine based on the
analysis of 35 cigarettes: (0.857, 1.124).
a. Provide and interpretation of this interval.
b. Explain how this interval can be used to test the researcher’s
hypothesis
c. State the conclusion of that hypothesis test.
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a. The 95% interval is (0.857, 1.124).
Confidence interval is a estimate of a population parameter. At a certain confidence level we say that the actual population parameter lies within an interval. So, a interval of (0.857,1.123) is interpreted as : We are 95% confident that the actual true concentration of nicotine in Cigarettes lies in this interval , between .857 and 1.124
b. This interval can be used by knowing whether a claimed amount lies within this interval. if it does, then the we fail to reject the null hypothesis, i.e. say that claim is correct. Here' 1 mg claim lies between 0.857 and 1.124, and thus we conclude that the claim can't be rejected, so its' "correct".
c. Conclusion:
true concentration of nicotine in cigarettes (in milligrams) is equal to the claimed amount of 1mg.
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