Question

You are interested in whether the average lifetime of Duracell AAA batteries is different from the average lifetime of Energizer AAA batteries. You lay out your hypotheses as follows: Null Hypothesis: μ₁ = μ₂, Alternative Hypothesis: μ₁ ≠ μ₂. After running a two independent samples t-test, you see a p-value of 0.2756. What is the appropriate conclusion?

Question options:

1)	The average lifetime of Duracell AAA batteries is significantly different from the average lifetime of Energizer AAA batteries.

2)	We did not find enough evidence to say the average lifetime of Duracell AAA batteries is greater than the average lifetime of Energizer AAA batteries.

3)	We did not find enough evidence to say a significant difference exists between the average lifetime of Duracell AAA batteries and the average lifetime of Energizer AAA batteries.

4)	We did not find enough evidence to say the average lifetime of Duracell AAA batteries is less than the average lifetime of Energizer AAA batteries.

5)	The average lifetime of Duracell AAA batteries is equal to the average lifetime of Energizer AAA batteries.

Answer 1

Decision rule based on p-value and given level of significance ( ) :

If level of significance is not given then take it as 0.05

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.2756 > 0.05 so we used 2nd rule.

That is we fail to reject null hypothesis

Conclusion: At 5% level of significance there are not sufficient evidence to support alternative hypothesis.

So correct option is 3.

We did not find enough evidence to say a significant difference exists between the average lifetime of Duracell AAA batteries and the average lifetime of Energizer AAA batteries.