A random sample of 14 cigarettes of a certain brand has an average nicotine content of 4.4 milligrams and a standard deviation of 2.2 milligrams. What is the standard error of the 99% confidence interval for the average nicotine content of the cigarettes. Note: Round your answer to 4 decimal places.
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Answer:
The standard error is a measure of the precision of the sample mean as an estimate of the population mean. It can be calculated using the formula:
Step-by-step explanation:
standard error = standard deviation / square root of sample size
In this case, we are given the sample standard deviation as 2.2 milligrams and the sample size as 14 cigarettes. So, we can calculate the standard error as:
standard error = 2.2 / sqrt(14)
standard error = 0.5877
Now, we need to calculate the 99% confidence interval for the population mean of nicotine content. For this, we can use the formula:
confidence interval = sample mean ± (critical value x standard error)
where the critical value corresponds to the level of confidence and degrees of freedom. Since we have a small sample size (n < 30), we need to use a t-distribution instead of a normal distribution. The degrees of freedom for a sample of size 14 is 13. To find the critical value, we can use a t-table or a calculator. For a 99% confidence interval and 13 degrees of freedom, the critical value is 2.6503.
Substituting the values, we get:
confidence interval = 4.4 ± (2.6503 x 0.5877)
confidence interval = 4.4 ± 1.5579
confidence interval = (2.8421, 5.9579)
Therefore, we can say with 99% confidence that the population mean of nicotine content for this brand of cigarettes is between 2.8421 and 5.9579 milligrams.
Haruki Nezugazawa.