Health Care Expenditures. The Health Care Cost Institute...

Health Care Expenditures. The Health Care Cost Institute tracks health care expenditures for beneficiaries under the age of 65 who are covered by employex-sponsored private health insurance. The data contained in the file DrugCost are consistent with the institute's findings concerning annual preseription costs per employee. Analyze the data using Excel and answer the following questions. a. Develop a $90 \%$ confidence interval for the annual cost of prescription drugs. b. Develop a $90 \%$ confidence interval for the amount of out-of-pocket expense per employee. c. What is your point estimate of the proportion of employees who incurred no prescription drug costs? d. Which, if either, of the confidence intervals in parts (a) and (b) has a larger margin of error. Why?

Health Care Expenditures. The Health Care Cost Institute tracks health care expenditures for beneficiaries under the age of 65 who are covered by employex-sponsored private health insurance. The data contained in the file DrugCost are consistent with the institute's findings concerning annual preseription costs per employee. Analyze the data using Excel and answer the following questions.
a. Develop a $90 \%$ confidence interval for the annual cost of prescription drugs.
b. Develop a $90 \%$ confidence interval for the amount of out-of-pocket expense per employee.
c. What is your point estimate of the proportion of employees who incurred no prescription drug costs?
d. Which, if either, of the confidence intervals in parts (a) and (b) has a larger margin of error. Why?

Key Concepts

Sampling Distribution

The sampling distribution of a statistic is the probability distribution of that statistic calculated from a large number of samples drawn from the same population. Understanding the sampling distribution is crucial for constructing confidence intervals as it provides the basis for quantifying the variability of the estimator and applying appropriate probability models, such as the normal or t-distribution.

Proportion Estimation

Proportion estimation involves determining the fraction or percentage of the sample that exhibits a certain characteristic, which is then used as an estimate of the population proportion. Confidence intervals for proportions are constructed using methods that account for the binomial nature of the data, often with adjustments for sample size and variability.

Point Estimate

A point estimate is a single value calculated from sample data that is used as a best guess for an unknown population parameter. It serves as the central value around which a confidence interval is constructed, and while it provides a specific estimate, it does not capture the uncertainty inherent in the sampling process.

Margin of Error

The margin of error quantifies the amount of random sampling error in a survey's results and represents the maximum expected difference between the true population parameter and a sample estimate. It is derived from the standard error and the critical value corresponding to the chosen confidence level, and it determines the width of the confidence interval.

Confidence Interval

A confidence interval is a range of values used to estimate a population parameter, such as a mean or a proportion, with an associated degree of confidence that the interval contains the true parameter value. The interval is calculated from sample data and expresses the uncertainty around the point estimate, typically incorporating factors like sample size, variability, and the chosen confidence level.

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