16. We test the null hypothesis H_0: μ=10 and the alternative H_a: μ<10, for a normal population with σ=4. A random sample of 16 observations is drawn from the population and we find the sample mean of these observations is 12. The $p$-value is closest to (A) 0.0228 (B) 0.0456 (C) 0.1016 (D) 0.9772 (E) 0.9999

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.

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