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

question 53

Essay

A random sample of 80 observations produced a mean $\bar { x } = 35.4$ and a standard deviation $s$ $= 3.1$ .
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:

Interdependence

A social and psychological concept referring to the way in which individuals depend on each other for the fulfillment of their needs, influencing their behaviors and attitudes in social contexts.

Insecure Attachment

A type of attachment style characterized by anxiety and uncertainty in relationships, often resulting from inconsistent caregiving in early life.

Caudate Nucleus

A brain structure known to play significant roles in learning, memory, reward processing, motivation, and movement.

Hippocampus

A region of the brain important for learning and memory, particularly in consolidating short-term memories into long-term memories.