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

question 107

Essay

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 $\sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 } \text {. Use } \alpha = 0.05 \text {. }$ $$\begin{array} { l } \text {Local Bank}\\\mathrm { n } _ { 1 } = 15 \\\overline { \mathrm { x } } 1 = 5.3 \text { minutes } \\\mathrm { s } _ { 1 } = 1.1 \text { minute }\end{array}$$ $$\begin{array} { l } \text {Competitor Bank}\\\mathrm { n } _ { 2 } = 16 \\\overline { \mathrm { x } } 2 = 5.6 \text { minutes } \\\mathrm { s } _ { 2 } = 1.0 \text { minutes }\end{array}$$

---

Definitions:

Kant

Immanuel Kant, an 18th-century German philosopher who is known for his work on deontological ethics, the theory of knowledge, and aesthetics.

Autonomy

Independence. Intellectual autonomy is the ability of a rational person to reach his or her own conclusions about what to believe and what not to believe. Moral autonomy is the ability of a rational person to reach his or her own moral conclusions about what is right and what is wrong. (This does not mean that people will necessarily come to different conclusions.)

Psychological

Pertaining to the mind or mental processes, often focusing on behavior, cognition, emotions, and the mental functions in individuals.

Kant

Refers to Immanuel Kant, an 18th-century German philosopher who made pivotal contributions to the development of modern philosophy, especially in the areas of epistemology and ethics.