Independent Random Samples from Normal Populations Produced the Results Shown $5.8,5.1,3.9,4.5,5.4$

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