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What would be the null/alternate hypotheses in this case and where would the critical region lie?H₀: μ ≥ 300 ppm and H₁: μ < 300 ppm; critical region lies on the left side of the tailH₀: μ < 300 ppm and H₁: μ ≥ 300 ppm;  critical region lies on the left side of the tailH₀: μ ≤ 300 ppm and H₁: μ > 300 ppm;  critical region lies on the left side of the tailH₀: μ > 300 ppm and H₁: μ ≤ 300 ppm;  critical region lies on the right side of the tail

Question

What would be the null/alternate hypotheses in this case and where would the critical region lie?H₀: μ ≥ 300 ppm and H₁: μ < 300 ppm; critical region lies on the left side of the tailH₀: μ < 300 ppm and H₁: μ ≥ 300 ppm;  critical region lies on the left side of the tailH₀: μ ≤ 300 ppm and H₁: μ > 300 ppm;  critical region lies on the left side of the tailH₀: μ > 300 ppm and H₁: μ ≤ 300 ppm;  critical region lies on the right side of the tail

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Solution

The null and alternate hypotheses, as well as the location of the critical region, depend on the specific research question and the direction of the expected effect. Here are the interpretations for each pair of hypotheses:

  1. H₀: μ ≥ 300 ppm and H₁: μ < 300 ppm; critical region lies on the left side of the tail. This means that we initially assume that the population mean is greater than or equal to 300 ppm. We are testing to see if the actual mean is less than 300 ppm. If our test statistic falls in the critical region on the left side of the distribution, we would reject the null hypothesis in favor of the alternate hypothesis.

  2. H₀: μ < 300 ppm and H₁: μ ≥ 300 ppm; critical region lies on the left side of the tail. This is incorrect because if we are testing whether the population mean is greater than or equal to 300 ppm, the critical region should be on the right side of the distribution.

  3. H₀: μ ≤ 300 ppm and H₁: μ > 300 ppm; critical region lies on the left side of the tail. This is also incorrect because if we are testing whether the population mean is greater than 300

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