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

Suman Cole 2021-01-19 Answered

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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## Expert Answer

lamusesamuset
Answered 2021-01-20 Author has 93 answers
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: "${H}_{0}:{\mu }_{1}\le {\mu }_{2},{H}_{a}:{\mu }_{1}>{\mu }_{2}$"
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