Question

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.

a. H0:μ1≥μ2; Ha:μ1<μ2
b. H0:μ1≤−μ2; Ha:μ1>−μ2
c. H0:μ1≥−μ2; Ha:μ1<−μ2
d. H0:μ1=μ2; Ha:μ1≠μ2
e. H0:μ1≤μ2; Ha:μ1>μ2

Answer 1

H0 : u1 = u2 ; H1 : u1 ≠ u2 , or specifically u1 > u2

Explanation:

Null Hypothesis is the neutral hypothesis , stating no difference from assumed value, (or in this case no difference between both batteries' mean life)

Alternate Hypothesis is the special case hypothesis, stating difference from assumed value , (or in this case states difference between both batteries' mean life)

Let mean life of battery 1 & battery be b = u1 & u2 , respectively.

Null Hypothesis [ H0 ] : u1 = u2

Alternate Hypothesis [ H1 ] : u1 ≠ u2 , or specifically u1 > u2 { To determine if battery 1 lasts longer than battery 2 }