Correct A biologist examines 15 sedimentary samples for lead concentration. The mean lead concentration for the sample data is $0.511 \mathrm{cc} / \mathrm{cubic}$ meter with a standard deviation of 0.0598 . Determine the $98 \%$ confidence interval for the population mean lead concentration. Assume the population is approximately normal. Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places. Answer How to enter your answer (opens in new window) Tables Keypad Keyboard Shortcuts Submit Answer

Step 1 ：A biologist examines 15 sedimentary samples for lead concentration. The mean lead concentration for the sample data is \(0.511 \, \mathrm{cc} / \mathrm{cubic}\) meter with a standard deviation of 0.0598. We are asked to determine the \(98\%\) confidence interval for the population mean lead concentration, assuming the population is approximately normal.

Step 2 ：The first step is to find the critical value that should be used in constructing the confidence interval. This is done by calculating the Z-score for a \(98\%\) confidence interval.

Step 3 ：The Z-score is calculated using the formula for the percentile of a normal distribution, which is given by the inverse of the cumulative distribution function. For a \(98\%\) confidence interval, we want the Z-score that corresponds to the \(99\%\) percentile, because the \(98\%\) confidence interval is the range between the \(1\%\) and \(99\%\) percentiles.

Step 4 ：Using the scipy.stats library in Python, the Z-score for the \(99\%\) percentile is calculated as follows: \(\text{z\_score} = \text{stats.norm.ppf}(0.99)\).

Step 5 ：The calculated Z-score is approximately \(2.326\).

Step 6 ：Final Answer: The critical value that should be used in constructing the \(98\%\) confidence interval is approximately \(\boxed{2.326}\).