15. A professor of statistics refutes the claim that the average student spends 3 hours studying for the midterm exam. The professor thinks the students spend more time than that. Which hypotheses are used to test the claim?
(A) \(H_0: \mu \leq 3\) vs. \(H_a: \mu > 3\)
(B) \(H_0: \mu = 3\) vs. \(H_a: \mu \neq 3\)
(C) \(H_0: \mu \neq 3\) vs. \(H_a: \mu = 3\)
(D) \(H_0: \mu = 3\) vs. \(H_a: \mu < 3\)
(E) \(H_0: \mu \geq 3\) vs. \(H_a: \mu = 3\)

16. We test the null hypothesis $H_0: \mu=10$ and the alternative $H_a: \mu

17. The nicotine content in cigarettes of a certain brand is normally distributed, with mean (in milligrams) and standard deviation $\sigma = 0.1$. The brand advertises that the mean nicotine content of its cigarettes is 1.5, but measurements on a random sample of 100 cigarettes of this brand give a mean of $\overline{x} = 1.53$. Is this evidence that the mean nicotine content is actually higher than advertised? To answer this, test the hypotheses $H_0: \mu = 1.5, H_a: \mu > 1.5$ at the 5% significance level. You conclude (A) That \(H_0\) should be rejected. (B) That \(H_0\) should not be rejected. (C) That \(H_{a}\) should be rejected. (D) There is a \(5\%\) chance that the null hypothesis is true. (E) There is a \(5\%\) chance that the alternative hypothesis is true.

18. A certain population follows a normal distribution with mean $\mu$ and standard deviation $\sigma = 2.5$. You collect data and test the hypotheses $H_0: \mu = 1, H_a: \mu \neq 1$. You obtain a $p$-value of 0.022. Which of the following is true? (A) A \(90\%\) confidence interval for \(\mu\) will include the value 1. (B) A \(95\%\) confidence interval for \(\mu\) will include the value 1. (C) A \(95\%\) confidence interval for \(\mu\) will include the value 0. (D) A \(99\%\) confidence interval for \(\mu\) will include the value 1. (E) A \(99\%\) confidence interval for \(\mu\) will include the value 0.

19. Suppose that the significant level of a statistical hypothesis test is $\alpha$. The null hypothesis will be rejected when: (A) \(p\)-value \(\leq \alpha\) (B) \(p\)-value \(>\alpha\) (C) \(p\)-value \(\leq \alpha / 2\) (D) \(p\)-value \(>\alpha / 2\) (E) \(p\)-value \(= \frac{\alpha}{2}\)

20. The average monthly rent for one-bedroom apartments in Chattanooga has been $700. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are (A) \(H_0: \mu \geq 700\) v.s. \(H_a: \mu < 700\) (B) \(H_0: \mu = 700\) v.s. \(H_a: \mu \neq 700\) (C) \(H_0: \mu > 700\) v.s. \(H_a: \mu \leq 700\) (D) \(H_0: \mu < 700\) v.s. \(H_a: \mu \geq 700\) (E) \(H_0: \mu < 700\) v.s. \(H_a: \mu > 700\) $^{1}$ For z ≥ 3.90, the areas are 1.0000 to four decimal places. Copyright 2010 Pearson Education, Inc.

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