A Local Bank Claims That the Waiting Time for Its $\alpha$

question 84

Essay

A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor
bank checks the waiting times at both banks. Use P-values to test the local bankʹs claim. Use $\alpha$ = 0.05. Assume
the two samples are random and independent. $$\begin{array} { cc} \text {Local Bank}&\text {Competitor Bank}\\\mathrm { n } _ { 1 } = 45 & \mathrm { n } _ { 2 } = 50 \\\overline { \mathrm { x } } 1 = 5.3 \text { minutes } & \overline { \mathrm { x } } 2 = 5.6 \text { minutes } \\\sigma _ { 1 } = 1.1 \text { minutes } & \sigma _ { 2 } = 1.0 \text { minutes }\end{array}$$

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Definitions:

Compounded Continuously

A method of calculating interest where the frequency of compounding is infinitely small, effectively occurring every moment, leading to exponential growth.

Stated Rate

The interest rate declared on a financial instrument, such as a bond or loan, without adjusting for compounding or fees.

Compounded Annually

A method of calculating interest where the interest earned or paid is added to the principal, resulting in interest on interest in subsequent periods.

Effective Rate

The interest rate on a loan or financial product, adjusted for the effect of compounding over a given period.