Step 1 :The given DNA base codes are 1, 1, 2, 4, 3, 4, 3, 4, 4, 2. We are asked to find the 95% confidence interval for the mean of these codes.
Step 2 :First, we calculate the sample mean (\(\bar{x}\)) of the DNA base codes, which is 2.8.
Step 3 :Next, we calculate the sample standard deviation (s) of the DNA base codes, which is approximately 1.23.
Step 4 :The sample size (n) is 10, as there are 10 DNA base codes.
Step 5 :We then use the formula for the confidence interval, which is \(\bar{x} \pm z \frac{s}{\sqrt{n}}\), where z is the z-score corresponding to the desired level of confidence. For a 95% confidence interval, the z-score is approximately 1.96.
Step 6 :Substituting the values into the formula, we get the 95% confidence interval for the population mean \(\mu\) as \(2.0 < \mu < 3.6\).
Step 7 :Final Answer: The 95% confidence interval for the population mean \(\mu\) is \(\boxed{2.0 < \mu < 3.6}\).
Step 8 :The practical use of the confidence interval is to estimate that, with 95% confidence, the interval from 2.0 to 3.6 actually contains the true mean DNA base of all people.