Question

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 yielded mean nicotine content of 27.3 milligrams and standard deviation of 2.1 milligrams for a sample of n = 9 cigarettes. Construct a 95% confidence interval for the mean nicotine content of this brand of cigarette.

Answer 1

To construct a 95% confidence interval for the mean nicotine content, use the formula: Confidence interval = mean ± (critical value) × (standard deviation / √n). The 95% confidence interval for the mean nicotine content of this brand of cigarettes is approximately (26.296, 28.304).

Step-by-step explanation:

To construct a 95% confidence interval for the mean nicotine content of the new brand of cigarettes, we can use the formula:

Confidence interval = mean ± (critical value) × (standard deviation / √n)

In this case, the mean nicotine content is 27.3 milligrams, the standard deviation is 2.1 milligrams, and the sample size is 9 cigarettes. The critical value for a 95% confidence interval is approximately 2.262 (based on a t-distribution).

Plugging these values into the formula, we get:

Confidence interval = 27.3 ± (2.262) × (2.1 / √9)

Simplifying the equation, we have:

Confidence interval = 27.3 ± 1.004

Therefore, the 95% confidence interval for the mean nicotine content of this brand of cigarettes is approximately (26.296, 28.304).