Question

Share with your peers the null and alternative hypotheses for a decision that is relevant to your personal or professional life (any example is fine). Remember in hypothesis testing the "equals" part corresponds to the null hypothesis, so you can have less than or equal to, greater than or equal to, or just equal to when defining the null hypothesis. The alternative hypothesis will then be either greater than, less than, or not equal to in relation to the above null criteria. See below for how it looks symbolically for the three possible setups.

I. H₀: μ ≥ μ₀; H_a: μ < μ₀
II. H₀: μ ≤ μ₀; H_a: μ > μ₀
III. H₀: μ = μ₀; H_a: μ ≠ μ₀

Note that a hypothesis test really needs to be set up to be testable, so be sure to have it presented in that manner where you are testing the μ₀ value. Additionally, identify the Type I and Type II errors that could occur with your decision‐making process.

Answer 1

Answer :-

Suppose we wants to test average life of light bulbs.

The Null hypothesis (H₀):

The average life of light bulbs 1000 hours.

That is , H₀: 1000

Vs.

The alternative hypothesis ( H₁):

That is , H_a : > 1000

Following errors will occur in the decision making process-

Type 1 error:- Rejecting the null hypothesis when it is true.

Type 2 error:- Do not reject the null hypothesis while alternative hypothesis is true.