Question

Identify the null and alternative hypotheses in the following scenario: To determine if running shoes 1 have the same durability as running shoes 2, the mean durability, in miles, of the two competing running shoes is compared. Fourteen runners are randomly assigned to test each type of shoe. Both populations have normal distributions with known standard deviations.

A. H₀:μ₁=μ₂;Hₐ:μ₁=μ₂
B. H₀:μ₁=μ₂;Hₐ:μ₁=μ₂
C. H₀:μ₁≥μ₂;Hₐ:μ₁<μ₂
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Answer 1

The null hypothesis is that the two types of running shoes have the same durability, and the alternative hypothesis is that they have different durabilities.

Step-by-step explanation:

The null hypothesis in this scenario is H₀: μ₁=μ₂ and the alternative hypothesis is Hₐ: μ₁≠μ₂.

In other words, the null hypothesis states that running shoes 1 and running shoes 2 have the same durability, while the alternative hypothesis states that they have different durabilities.

This is a two-sample hypothesis test comparing the mean durability of the two types of running shoes, and the populations have normal distributions with known standard deviations.