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

question 84

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 $\left( \mu _ { 1 } - \mu _ { 2 } \right)$ .

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Definitions:

Growth Patterns

Growth patterns refer to the characteristic ways in which individuals grow and develop physically over time, often studied to understand health, nutritional needs, and developmental progress.

Infants

Very young children, especially those from birth to one year of age, experiencing rapid physical and cognitive development.

Neonates

Newborn infants, especially within the first month after birth, emphasizing the earliest phase of life outside the womb.

Cephalocaudal Development

A pattern of growth where development proceeds from the head downward through the body.