Independent Random Samples from Normal Populations Produced the Results Shown $\sigma ^ { 2 }$

question 38

Essay

Independent random samples from normal populations produced the results shown below. Sample 1: 5.8, 5.1, 3.9, 4.5, 5.4 Sample 2: 4.4, 6.1, 5.2, 5.7 a. Calculate the pooled estimator of $\sigma ^ { 2 }$ .
b. Test $\mu _ { 1 } < \mu _ { 2 }$ using $\alpha = .10$ .
c. Find a $90 \%$ confidence interval for $\left( \mu _ { 1 } - \mu _ { 2 } \right)$ .

---

Definitions:

Obsessive-Compulsive

A condition characterized by intrusive thoughts that produce uneasiness, apprehension, fear, or worry; and behaviors aimed at reducing the anxiety associated with these obsessions.

Anxiety Disorders

A collection of psychological disorders marked by intense anxiety and fear that affect everyday activities.

Psychotic Disorders

A spectrum of mental health disorders characterized by detachment from reality, typically evidenced by delusions, hallucinations, disorganized thinking, and speech.

Etiology

refers to the study of the causes or origins of diseases or conditions, looking into factors that contribute to their development.