Question

6. 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.

Answer 1

a) Based on the confidence interval at 95% confidence level on the analysis of 35 cigarettes we can say that we are 95% confident that the mean amount of nicotine true concentration is inside the calculated interval.

b) According to the claim the true concentration of nicotine is 1mg.

The hypotheses can be setup as:

Ho : mean = 1mg

Ha : Mean is not equal to 1mg.

So, base on interval we can test the hypothesis that whether we can reject the null hypothesis or not. And based on the rejection of hypothesis we can have the evidence that we can support or not the claim.

C) Conclusion

As the interval includes that 1mg values we cannot reject the null hypothesis and would say that we do not have enough evidence to warrant the claim.