Question

A5) 45) To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette gave a mean nicotine content of 2 milligrams and standard deviation of 2.1 milligrams for a sample of n 9 cigarettes. The FDA e, and their claims that the mean nicotine content exceeds 28.6 milligrams for this brand of cigarett stated reliability is 98%. Do you agree? A) Yes, since the value 286 does not fall in the 98% confidence interval. B) Yes, since the value 28 6 does fall in the 98% confidence interval. C) No, since the value 286 does not fall in the 98% confidence interval. D) No, since the value 286 does fall in the 98% confidence interval

Answer 1

Here

sample mean $\bar{x} = 25.6$

sample standard deviation

and sample size

a 98% confidence interval for mean nicotine contest

$=(\bar{x} - \frac{s}{\sqrt{n}}*t_{0.01,n-1}, \bar{x} + \frac{s}{\sqrt{n}}*t_{0.01,n-1})$

2.1 = (25.6--* t0.01.8 , 2 (25.6-21 Vg tao1,s,23.0 +001,s

$=(25.6 - \frac{2.1}{\sqrt{9}}*2.89646, 25.6 + \frac{2.1}{\sqrt{9}}*2.89646)$

$=(23.5725,27.6275)$

ans-> c) No, since the value 28.6 does not fall in the 98% confidence interval.