Question

A new cigarette has recently been marketed. Tests by on the Food and Drug Administration (FDA) this cigarette gave a mean nicotine content of 24.6 milligrams and standard deviation of 2.4 milligrams for a sample of n = 9 cigarettes. The FDA claims that the mean nicotine content is different from 28.3 milligrams for this brand of cigarette, and their stated reliability is 99%. Assuming that X~Normal, they obtained a confidence interval of (21.92, 27.28). Would you accept the FDA's claim?

A. Yes

B. No

Answer 1

Given that the obtained 99% confidence interval of (21.92, 27.28)

and claim is that the mean nicotine content is different from 28.3 milligrams for this brand of cigarette

it is clear that the confidence interval limits are

lower limit = 21.92 < 28

and

upper limit = 27.28 < 28

So, we can see that both confidence interval limits are below the claimed value of 28

This shows that the difference is significant and the claim is supported by the confidence because the confidence interval does not include 28

So, answer is Yes, I will accept the FDA's claim