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 cigarettes. Construct a 95% confidence interval for the mean nicotine content of this brand of cigarette.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (± .025) and its Z score = 1.96
95% = mean ± 1.96 SEm
SEm = SD/√n
To construct a confidence interval for the mean nicotine content of the brand of cigarette, we can use the formula:
Confidence interval = sample mean +/- (critical value * standard error)
1. Find the critical value: Since we want a 95% confidence level, we need to find the z-score that corresponds to a 95% confidence level. This critical value can be found using a standard normal distribution table or a statistical calculator. For a 95% confidence level, the critical value is approximately 1.96.
2. Calculate the standard error: The standard error is a measure of the variability in the sample mean. It is calculated as the standard deviation divided by the square root of the sample size.
Standard error = (standard deviation) / sqrt(sample size)
= 2.1 / sqrt(sample size)
3. Plug in the values into the formula:
Confidence interval = sample mean +/- (critical value * standard error)
= 27.3 +/- (1.96 * (2.1 / sqrt(sample size)))
Since the sample size is not mentioned in the question, we cannot calculate an exact confidence interval without knowing the sample size. If you have the sample size, plug it into the formula to calculate the confidence interval.