This question tests hypothesis setup for a one-sample population mean test regarding lead concentration in water. The water department claims a mean of 5 ppb, and the researcher wants to check if it's different, implying a two-tailed test with H₀: μ = 5 vs. Hₐ: μ ≠ 5 to capture any deviation. This aligns perfectly with the 'different from' language, using the population mean μ and the claimed value in the null. Distractors include one-tailed tests that assume a specific direction (like >5), using the sample mean (5.8 ppb) in hypotheses, employing ar{x} instead of μ, or switching to a proportion test with p, which doesn't fit since lead concentration is a quantitative mean, not a proportion. Mini-lesson: For non-directional suspicions ('different' or 'changed'), use a two-sided alternative Hₐ: μ ≠ μ₀, where μ₀ is the stated value. Always focus on the population parameter μ, not sample statistics. This setup allows evidence to support rejection of the null if the mean is either higher or lower than claimed.

This question tests setting up a two-tailed hypothesis test for a population mean. The transit agency reports a mean of 12 minutes, giving us H₀: μ = 12. Since the group wants to test if the mean is 'different from' 12 minutes (not specifically higher or lower), we need a two-tailed test: Hₐ: μ ≠ 12. Option B incorrectly reverses the null and alternative hypotheses. Option C uses x̄ (sample mean) instead of μ (population mean) in the hypotheses. Option D uses p, which is for proportions, not means. Option E incorrectly uses the sample mean value (13.1) in the hypotheses—we test the claimed value, not the observed value. For 'different from' questions, always use ≠ in the alternative hypothesis.

This question involves setting up a left-tailed test for a population mean. The manufacturer claims μ = 18.0 ounces, which becomes our null hypothesis: H₀: μ = 18.0. The inspector wants to test if the true mean is less than 18.0 ounces, so we use a left-tailed alternative: Hₐ: μ < 18.0. Option B incorrectly uses the sample mean (17.8) in the hypotheses—we test claims about population parameters, not sample statistics. Option C has the inequality in H₀ pointing the wrong way for a 'less than' test. Option D uses x̄ instead of μ for the population parameter. Option E uses p, which is for proportions, not means. When the research question asks about 'less than,' use < in the alternative hypothesis.

This question requires setting up a right-tailed hypothesis test for a population mean. The manufacturer states the mean is 80 minutes, so H₀: μ = 80. The reviewer wants to test if the true mean is greater than 80 minutes, making this a right-tailed test with Hₐ: μ > 80. Option B incorrectly uses the sample mean value (84) in the hypotheses—we test the claimed population value. Option C uses x̄ (sample mean) instead of μ (population mean). Option D uses p, which is for proportions, not means. Option E has an inequality in H₀ and reverses the direction of the test. For 'greater than' questions, the alternative hypothesis uses > to indicate the direction of interest.

This question involves setting up a left-tailed test for a population mean. The dining hall claims the mean sodium content is 900 mg, so H₀: μ = 900. The student wants to test if the true mean is less than 900 mg, making this a left-tailed test with Hₐ: μ < 900. Option A incorrectly uses the sample mean value (872) in the null hypothesis—we test the claimed value, not the observed value. Option C has the wrong direction in the alternative hypothesis (> instead of <). Option D uses x̄ instead of μ for the population parameter. Option E uses p, which is for proportions, not means. Remember that hypothesis tests always involve population parameters (μ) and test claimed values, not sample statistics.

This question tests understanding of how to translate "no more than" into proper hypotheses. The claim "no more than 9 grams" means μ ≤ 9 grams. When testing against such a claim, the null hypothesis includes this inequality (H₀: μ ≤ 9), and the alternative hypothesis represents the opposite direction (Hₐ: μ > 9). This tests whether the cereal exceeds the stated sugar limit. Option A incorrectly uses equality in the null with a two-sided alternative. Option C tests in the wrong direction. Option D incorrectly uses x̄ instead of μ and includes the sample statistic in the hypothesis. Option E incorrectly uses p (proportion) instead of μ. The correct answer B properly sets up H₀: μ ≤ 9 g vs. Hₐ: μ > 9 g to test if the mean sugar content exceeds the label's claim.

This question focuses on hypothesizing for a one-sample mean test about sugar content in granola bars. The label claims 12 grams mean, but the dietitian suspects more, warranting a right-tailed test: H₀: μ = 12 vs. Hₐ: μ > 12, using μ for the population mean and the claimed value in the null. This matches the 'more than' suspicion directly. Distractors feature the sample mean (12.7 grams) in the null, wrong direction (like <12), using ar{x} symbols inappropriately, or testing a proportion p, which is incorrect for a mean measurement like grams of sugar. Mini-lesson: Set up the null as H₀: μ = claimed value, and for suspicions of excess ('more' or 'higher'), use Hₐ: μ > μ₀. Sample results like the mean of 12.7 inform the p-value calculation, not the hypotheses. This structure tests if evidence supports the alternative over the null claim.

This problem involves setting up a left-tailed test for a population mean. The hospital claims μ = 3.5 days, which forms our null hypothesis: H₀: μ = 3.5. The researcher wants to test if the true mean is less than 3.5 days, so we use a left-tailed alternative: Hₐ: μ < 3.5. Option B incorrectly uses the sample mean (3.2) in the hypotheses—we test claims about the population parameter, not sample statistics. Option C has an inequality in H₀ and points in the wrong direction for a 'less than' test. Option D uses x̄ instead of μ for the population parameter. Option E uses p (for proportions) instead of μ (for means). When testing if something is 'less than' a claimed value, use < in the alternative hypothesis.

This question requires setting up a two-tailed test for a population mean. The null hypothesis states the claimed value: H₀: μ = 10.0 hours. Since the engineer wants to test if the mean is 'different from' 10.0 hours (not specifically greater or less), we need a two-tailed alternative: Hₐ: μ ≠ 10.0. Option B incorrectly uses the sample mean value (9.6) in the hypotheses—we always test claims about the population parameter, not sample statistics. Option C incorrectly uses x̄ instead of μ. Option D uses p (for proportions) instead of μ. Option E reverses the null and alternative hypotheses. Remember that for 'different from' questions, use a two-tailed test with ≠ in the alternative hypothesis.

This problem tests setting up a two-tailed hypothesis test for a population mean. The cooperative claims μ = 150 grams, which becomes our null hypothesis: H₀: μ = 150. Since they want to test if the mean is 'different from' 150 grams (not specifically heavier or lighter), we need a two-tailed alternative: Hₐ: μ ≠ 150. Option B incorrectly uses the sample mean (151.6) in the hypotheses—we test claims about population parameters. Option C uses p (for proportions) instead of μ (for means). Option D reverses the null and alternative hypotheses. Option E uses x̄ instead of μ for the population parameter. When the question asks about 'different from,' always use a two-tailed test with ≠ in the alternative hypothesis.