/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 An individual can take either a ... [FREE SOLUTION] | 91影视

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Chapter 11: Problem 2

An individual can take either a scenic route to work or a nonscenic route. She decides that use of the nonscenic route can be justified only if it reduces the mean travel time by more than 10 minutes. a. If \(\mu_{1}\) is the mean for the scenic route and \(\mu_{2}\) for the nonscenic route, what hypotheses should be tested? b. If \(\mu_{1}\) is the mean for the nonscenic route and \(\mu_{2}\) for the scenic route, what hypotheses should be tested?

Short Answer

Expert verified
a. Null Hypothesis: \(H_{0}: \mu_{1}-\mu_{2} \leq 10\), Alternative Hypothesis: \(H_{a}: \mu_{1}-\mu_{2} > 10\). b. Null Hypothesis: \(H_{0}: \mu_{2}-\mu_{1} \geq -10\), Alternative Hypothesis: \(H_{a}: \mu_{2}-\mu_{1} < -10\).

Step by step solution

01

Formulate Hypothesis for Scenario a

In part a, it is required to test whether the nonscenic route reduces travel time by more than 10 minutes compared to the scenic route. Formulate the hypothesis as follows:\Null Hypothesis, \(H_{0}: \mu_{1}-\mu_{2} \leq 10\), i.e. the non-scenic route does not decrease travel time by more than 10 minutes.\Alternative Hypothesis, \(H_{a}: \mu_{1}-\mu_{2} > 10\), i.e. the non-scenic route decreases travel time by more than 10 minutes.
02

Formulate Hypothesis for Scenario b

In part b, if \(\mu_{1}\) is the mean of the nonscenic route and \(\mu_{2}\) is the mean of the scenic route, then the hypotheses should be formulated by interpolating the given condition.\Null Hypothesis, \(H_{0}: \mu_{2}-\mu_{1} \geq -10\), i.e. the non-scenic route does not decrease the travel time by more than 10 minutes.\Alternative Hypothesis, \(H_{a}: \mu_{2}-\mu_{1} < -10\), i.e. the non-scenic route decreases travel time by more than 10 minutes.

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