# Identify the null and alternative hypothesis in the following scenario.

Identify the null and alternative hypothesis in the following scenario.
To determine if battery 1 lasts longer than battery 2, the mean lasting times, of the two competing batteries are compared. Twenty batteries of each type are randomly sampled and tested. Both populations have normal distributions with unknown standard deviations.
Select the correct answer below: ${H}_{0}:{\mu }_{1}\ge {\mu }_{2},{H}_{a}:{\mu }_{1}<{\mu }_{2}$
${H}_{0}:{\mu }_{1}\le -{\mu }_{2},{H}_{a}:{\mu }_{1}>-{\mu }_{2}$
${H}_{0}:{\mu }_{1}\ge -{\mu }_{2},{H}_{a}:{\mu }_{1}<-{\mu }_{2}$
${H}_{0}:{\mu }_{1}={\mu }_{2},{H}_{a}:{\mu }_{1}\ne {\mu }_{2}$
${H}_{0}:{\mu }_{1}\le {\mu }_{2},{H}_{a}:{\mu }_{1}>{\mu }_{2}$

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Step 1: Given information
Twenty batteries of each type are randomly sampled and tested. Both populations have normal distributions with unknown standard deviations.
Step 2: Answer is given by,
Null hypothesis: ${H}_{0}:{\mu }_{1}\le {\mu }_{2}$
Alternative hypothesis: ${H}_{a}:{\mu }_{1}>{\mu }_{2}$
Option (5) is correct.
Result: "${H}_{0}:{\mu }_{1}\le {\mu }_{2},{H}_{a}:{\mu }_{1}>{\mu }_{2}$"