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

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