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The state lottery office claims that the average household income of those people playing the lottery is at least $37,000.Assume that the distribution of household income of those people playing the lottery is normally distributed with a standard deviation of $5,756.Suppose that for a sample of 25 households,it is found that the average income was $36,243.
-What are the appropriate null and alternative hypotheses?

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Quizplus · Accepted Answer

The null hypothesis (H0) is a statement of no effect or no difference, and it often represents a statement of equality. In this case, the null hypothesis is that the average household income of those playing the lottery is at least $37,000, which can be represented as μ ≥ $37,000. However, since hypothesis tests typically involve equality in the null hypothesis, it is more accurate to state H0: μ = $37,000 for the purpose of conducting the test. The alternative hypothesis (H1 or Ha) is what you might believe to be true or hope to prove true. In this scenario, the claim to be tested is whether the average income is less than $37,000, based on the sample data. Therefore, the alternative hypothesis should be H1: μ < $37,000, which suggests that the average income is less than the state lottery office's claim. This makes option C the correct choice, as it correctly sets up the null hypothesis as stating the average is $37,000 and the alternative hypothesis as the average being less than $37,000.

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