Im kind of confused on this 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 recently been marketed. The FDA tests on this cigarette gave a mean nicotine content of 26.7 milligrams and standard deviation of 2.2 milligrams for a sample of n = 9 cigarettes. The FDA claims that the mean nicotine content exceeds 30.2 milligrams for this brand of cigarette,

and their stated reliability is 99%. Do you agree? Explain.

I too am confused. The FDA's tested mean is below their "standard" of 30.2. How could they possibly conclude the acutual mean above 30.2??

To determine whether or not we agree with the FDA's claim that the mean nicotine content exceeds 30.2 milligrams for this brand of cigarette, we need to perform a hypothesis test.

Here are the steps to conduct the hypothesis test:

Step 1: State the null hypothesis (H0) and the alternative hypothesis (Ha).
- Null hypothesis (H0): The mean nicotine content is equal to or less than 30.2 milligrams (µ ≤ 30.2).
- Alternative hypothesis (Ha): The mean nicotine content exceeds 30.2 milligrams (µ > 30.2).

Step 2: Set the significance level (α).
The stated reliability is 99%, which means the significance level (α) is 1% or 0.01.

Step 3: Collect sample data and calculate the test statistic.
The mean nicotine content for the sample of 9 cigarettes is 26.7 milligrams, and the standard deviation is 2.2 milligrams.

Step 4: Determine the critical value or p-value.
To make this determination, we need to know the distribution of the test statistic. Since the sample size is small (n < 30) and the population standard deviation is unknown, we should use a t-distribution.

Degrees of freedom (df) for a one-sample t-test is given by (n - 1), where n is the sample size. In this case, df = 9 - 1 = 8.

Using the t-distribution with df = 8 and the one-sided test for Ha (µ > 30.2), we can find the critical value from a t-table or use statistical software.

Step 5: Compare the test statistic to the critical value or p-value.
If the test statistic is greater than the critical value or if the p-value is less than the significance level (α), then we reject the null hypothesis (H0). Otherwise, we fail to reject the null hypothesis (H0).

Step 6: State the conclusion.
Based on the comparison in step 5, we can make a conclusion whether to agree or disagree with the FDA's claim.

To complete the hypothesis test, we would need the test statistic and the critical value or p-value. Unfortunately, the question does not provide this information. Therefore, we cannot definitively agree or disagree with the FDA's claim without conducting the actual hypothesis test or having more information.