A Local Bank Claims That the Waiting Time for Its $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 } \text {, and (b) }$

A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitorʹs
bank checks the waiting times at both banks. Assume the samples are random and independent, and the
populations are normally distributed. Test the local bankʹs claim: (a)assuming that $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 } \text {, and (b) }$ assuming that $\sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 } \text {. Use } \alpha = 0.05 \text {. }$ $$\begin{array} { l } \text {Local Bank}\\\mathrm { n } _ { 1 } = 15 \\\overline { \mathrm { x } } 1 = 5.3 \text { minutes } \\\mathrm { s } _ { 1 } = 1.1 \text { minute }\end{array}$$ $$\begin{array} { l } \text {Competitor Bank}\\\mathrm { n } _ { 2 } = 16 \\\overline { \mathrm { x } } 2 = 5.6 \text { minutes } \\\mathrm { s } _ { 2 } = 1.0 \text { minutes }\end{array}$$