A psychologist wants to test if the mean reaction time for drivers under 2525 years is less than that for drivers 2525 years and older. The sample mean for 3535 younger drivers is 0.620.62 seconds (population standard deviation 0.080.08), and for 3838 older drivers is 0.680.68 seconds (population standard deviation 0.090.09). At α=0.10 \alpha = 0.10 , what are the null and alternative hypotheses for this test?

{H0:μ1−μ2≥0Ha:μ1−μ20\left\{\begin{array}{l} $$H_0$$: \$$mu_1$$ - \$$mu_2$$ \ge 0 \\ H_a: \$$mu_1$$ - \$$mu_2$$

0 \\ H_a: \$$mu_1$$ - \$$mu_2 = 0$$ \end{array}\right."\u003e{H0:μ1−μ2\u003e0Ha:μ1−μ2=0\left\{\begin{array}{l} $$H_0$$: \$$mu_1$$ - \$$mu_2$$ \u003e 0 \\ H_a: \$$mu_1$$ - \$$mu_2 = 0$$ \end{array}\right.

{H0:μ1−μ2=0Ha:μ1−μ20\left\{\begin{array}{l} $$H_0$$: \$$mu_1$$ - \$$mu_2 = 0$$ \\ H_a: \$$mu_1$$ - \$$mu_2$$

{H0:μ1−μ2=0Ha:μ1−μ2≠0\left\{\begin{array}{l} $$H_0$$: \$$mu_1$$ - \$$mu_2 = 0$$ \\ H_a: \$$mu_1$$ - \$$mu_2$$ \ne 0 \end{array}\right.

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Problem 17Multiple Choice

A psychologist wants to test if the mean reaction time for drivers under $25$ years is less than that for drivers $25$ years and older. The sample mean for $35$ younger drivers is $0.62$ seconds (population standard deviation $0.08$ ), and for $38$ older drivers is $0.68$ seconds (population standard deviation $0.09$ ). At $alpha equals 0.10$ , what are the null and alternative hypotheses for this test?

${\begin{matrix} H_{0} : μ_{1} - μ_{2} > 0 \\ H_{a} : μ_{1} - μ_{2} = 0 \end{matrix}$

${\begin{matrix} H_{0} : μ_{1} - μ_{2} = 0 \\ H_{a} : μ_{1} - μ_{2} < 0 \end{matrix}$

${\begin{matrix} H_{0} : μ_{1} - μ_{2} = 0 \\ H_{a} : μ_{1} - μ_{2} \neq 0 \end{matrix}$

${\begin{matrix} H_{0} : μ_{1} - μ_{2} \geq 0 \\ H_{a} : μ_{1} - μ_{2} < 0 \end{matrix}$

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