## Estimating Population Parameters from Ceramic Vessel Rim Diameters: An Archaeological Study### IntroductionArchaeologists at the Wind Mountain archaeological site have been studying the rim diameters of ceramic vessels. By analyzing sherds of clay vessels, researchers aim to reconstruct the original sizes of the ceramic artifacts. Below, we discuss the process used to estimate the population parameters based on a sample of rim diameters.### Sample DataA random sample of ceramic vessel rim diameters (in centimeters) was collected at the site. The sample data is as follows:\[ 15.9, 13.4, 22.1, 12.7, 13.1, 19.6, 11.7, 13.5, 17.7, 18.1 \]### Statistical Calculations#### (a) Determining the Sample Mean and Standard DeviationUsing a calculator, you can find the sample mean ($\overline{x}$) and the sample standard deviation ($s$). Remember to round your answers to four decimal places.\[ \overline{x} = \_\_\_\_ \, \text{cm} \]\[ s = \_\_\_\_ \, \text{cm} \]#### (b) Constructing a 95% Confidence IntervalTo estimate the population mean ($\mu$) of rim diameters for ceramic vessels, we can compute a 95% confidence interval. This interval provides a range within which we expect the true population mean to lie, with 95% certainty. Round your answers to one decimal place.\[ \text{Lower limit} = \_\_\_\_ \, \text{cm} \]\[ \text{Upper limit} = \_\_\_\_ \, \text{cm} \]### Steps to Compute the Statistics:1. **Calculate the Sample Mean ($\overline{x}$):** \[ \overline{x} = \frac{\sum x_i}{n} \] where $ \sum x_i $ is the sum of the sample measurements, and $ n $ is the sample size.2. **Calculate the Sample Standard Deviation (s):** \[ s = \sqrt{\frac{\sum (x_i - \overline{x})^2}{n-1}} \] Here, $ x_i $ represents each individual

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Description: ## Estimating Population Parameters from Ceramic Vessel Rim Diameters: An Archaeological Study### IntroductionArchaeologists at the Wind Mountain archaeological site have been studying the rim diameters of ceramic vessels. By analyzing sherds of cla

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Sherds of clay vessels were put together to reconstruct rim diameters of the original ceramic vessels at the Wind Mountain archaeological sitet. A random sample of ceramic vessels gave the following rim diameters (in centimeters). 15.9 13.4 22.1 12.7 13.1 19.6 11.7 13.5 17.7 18.1 A USE SALT (a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to four decimal places.) cm cm (b) Compute a 99% confidence interval for the population mean u of rim diameters for such ceramic vessels found at the Wind Mountain archaeological site. (Round your answers to one decimal place.) lower limit cm upper limit cm

Sherds of clay vessels were put together to reconstruct rim diameters of the original ceramic vessels at the Wind Mountain archaeological sitet. A random sample of ceramic vessels gave the following rim diameters (in centimeters). 15.9 13.4 22.1 12.7 13.1 19.6 11.7 13.5 17.7 18.1 A USE SALT (a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to four decimal places.) cm cm (b) Compute a 99% confidence interval for the population mean u of rim diameters for such ceramic vessels found at the Wind Mountain archaeological site. (Round your answers to one decimal place.) lower limit cm upper limit cm

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