μ₀ is known as the null hypothesis. This is the hypothesis that we are testing to determine if it is true, or false. If it is true, we accept the null hypothesis, if it is false, then we reject the null hypothesis.
μ₁ is known as the alternative hypothesis. This is the hypothesis that can be used if the null hypothesis (μ₀) is rejected.
The null hypothesis (μ₀) is said to be equal to 1 gallon. That is because we are testing the credibility of the statement "each can of paint contains 1 gallon". The alternative hypothesis (μ₁) states that the actual amount of paint in the can is less than 1 gallon. So if the null hypothesis is rejected, then the alternative hypothesis must be true.
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