The principal of a middle school claims that test scores of the seventh-graders at her school vary less than the test scores of seventh-graders at a neighboring school, which have variation described by $\sigma = 14.7$. A) $\begin{array}{l} H_{0}: \sigma=14.7 \ H_{1}: \sigma14.7 \end{array}$ C) $\begin{array}{l} \mathrm{H}_{0}: \sigma14.7 \end{array}$ D) $\begin{array}{l} \mathrm{H}_{0}: \sigma14.7 \ \mathrm{H}_{1}: \sigma \leq 14.7 \end{array}$

Question

The principal of a middle school claims that test scores of the seventh-graders at her school vary less than the test scores of seventh-graders at a neighboring school, which have variation described by $\sigma = 14.7$. A) $\begin{array}{l} H_{0}: \sigma=14.7 \ H_{1}: \sigma<14.7 \end{array}$ B) $\begin{array}{l} \mathrm{H}_{0}: \sigma=14.7 \ \mathrm{H}_{1}: \sigma>14.7 \end{array}$ C) $\begin{array}{l} \mathrm{H}_{0}: \sigma<14.7 \ \mathrm{H}_{1}: \sigma>14.7 \end{array}$ D) $\begin{array}{l} \mathrm{H}_{0}: \sigma>14.7 \ \mathrm{H}_{1}: \sigma \leq 14.7 \end{array}$

Quizplus · Accepted Answer

The null hypothesis $H_0$ should state that the variation is equal to the neighboring school's variation ($\sigma = 14.7$), and the alternative hypothesis $H_1$ should state that the variation is less ($\sigma < 14.7$), as claimed by the principal.

The Principal of a Middle School Claims That Test Scores σ=14.7\sigma = 14.7σ=14.7

The Principal of a Middle School Claims That Test Scores $\sigma = 14.7$