A Random Sample of 80 Observations Produced a Mean $\bar { x } = 35.4$

question 115

Essay

A random sample of 80 observations produced a mean $\bar { x } = 35.4$ and a standard deviation $= 3.1$ .
a. Find a $90 \%$ confidence interval for the population mean $\mu$ .
b. Find a $95 \%$ confidence interval for $\mu$ .
c. Find a $99 \%$ confidence interval for $\mu$ .
d. What happens to the width of a confidence interval as the value of the confidence coefficient is increased while the sample size is held fixed?

---

Definitions:

Metabolic Syndrome

A cluster of conditions—increased blood pressure, high blood sugar, excess body fat around the waist, and abnormal cholesterol levels—that occur together, increasing your risk of heart disease, stroke, and diabetes.

Type 1 Diabetes

An autoimmune condition where the pancreas produces little or no insulin, requiring daily insulin administration for management.

Cardiovascular Disease

This category includes medical conditions impacting the heart or the circulatory system, like coronary artery disease, hypertension, and strokes.

Education Level

The highest degree or grade of schooling an individual has completed.