SCENARIO 10-13
the Amount of Time Required to Reach a Customer

SCENARIO 10-13
The amount of time required to reach a customer service representative has a huge impact on
customer satisfaction. Below is the Excel output from a study to see whether there is evidence of a
difference in the mean amounts of time required to reach a customer service representative between
two hotels. Assume that the population variances in the amount of time for the two hotels are not
equal. $$\begin{array}{l}\text { t-Test: Two-Sample Assuming Unequal Variances }\\\begin{array} { l r r } \hline & { \text { Hotel 1 } } & { \text { Hotel 2 } } \\\hline \text { Mean } & 2.214 & 2.0115 \\\text { Variance } & 2.951657 & 3.57855 \\\text { Observations } & 20 & 20 \\\text { Hypothesized Mean Difference } & 0 & \\\text { df } & 38 & \\\text { t Stat } & 0.354386 & \\\text { P(T<=t) one-tail } & 0.362504 & \\\mathrm { t } \text { Critical one-tail } & 1.685953 & \\\mathrm { P } ( \mathrm { T } < = \mathrm { t } ) \text { two-tail } & 0.725009 & \\\mathrm { t } \text { Critical two-tail } & 2.024394 & \\\hline\end{array}\end{array}$$
-Referring to Scenario 10-13, state the null and alternative hypotheses for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer
Service representative between the two hotels. a) $H _ { 0 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } \geq 0$ versus $H _ { 1 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } < 0$
b) $H _ { 0 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } \leq 0$ versus $H _ { 1 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } > 0$
c) $H _ { 0 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } = 0$ versus $H _ { 1 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } \neq 0$
d) $H _ { 0 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } \neq 0$ versus $H _ { 1 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } = 0$

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