An alternative hypothesis in a one-sample Z-test could be represented as follows: A) $$H _ { 1 } : \bar { X } \mu$$ B) $$H _ { 0 } : \bar { X } \mu$$ C) $$H _ { 0 } : \bar { X } = \mu$$ D) $$H _ { 0 } : \bar { X }

Question

An alternative hypothesis in a one-sample Z-test could be represented as follows:
A) $$H _ { 1 } : \bar { X } > \mu$$
B) $$H _ { 0 } : \bar { X } > \mu$$
C) $$H _ { 0 } : \bar { X } = \mu$$
D) $$H _ { 0 } : \bar { X } < \mu$$

Quizplus · Accepted Answer

The alternative hypothesis in a one-sample Z-test is the hypothesis that the sample mean is not equal to the population mean. This can be represented as $$H _ { 1 } : \bar { X } \neq \mu$$. However, the question asks for the alternative hypothesis to be represented as $$H _ { 1 } : \bar { X } > \mu$$, which is a specific case of the general alternative hypothesis. Therefore, the correct answer is A.

An Alternative Hypothesis in a One-Sample Z-Test Could Be Represented H1:Xˉ>μH _ { 1 } : \bar { X } > \muH1​:Xˉ>μ

An Alternative Hypothesis in a One-Sample Z-Test Could Be Represented $H _ { 1 } : \bar { X } > \mu$