The nicotine content in cigarettes of a certain brand is Normally distributed with a standard deviation...
The nicotine content in cigarettes of a certain brand is Normally distributed with a standard deviation of σ = 0.1 milligrams. The brand advertises that the mean nicotine content of their cigarettes is μ = 1.5, but you are suspicious and plan to investigate the advertised claim by testing the hypotheses H0 : μ = 1.5 versus Ha : μ > 1.5 at the 5% significance level. You will do so by measuring the nicotine content of 15 randomly selected cigarettes of this brand and computing the mean nicotine content x ̄ of your measurements.
(a) What is the smallest value of x ̄ for which you will reject
H0?
(b) If the mean nicotine content of the cigarettes is, in fact, μ =
1.6, what is the power of the test?
(c) Draw a picture to illustrate parts (a) and (b).
Homework Answers
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The nicotine content in cigarettes of a certain brand is
Normally distributed with a standard deviation...
(1 point) The nicotine content in cigarettes of a certain brand is normally distributed with mean...
(1 point) The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) μ and standard deviation σ=0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5 mg. Now, suppose a reporter wants to test whether the mean nicotine content is actually higher than advertised. He takes measurements from a random sample of 15 cigarettes of this brand. The sample yields an average of 1.4 mg of nicotine. Conduct a test...
3. The nicotine content in cigarettes of a certain brand is normally distributed with mean (in...
3. The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) 4. The brand advertises that the mean nicotine content of their cigarettes is 1.5, but measurements on a random sample of 100 cigarettes of this brand gave a mean of r = 1.53 and standard deviation s=0.1. Is there sufficient evidence in the sample to suggest that the mean nicotine content is actually higher than advertised? Use a = 0.05. (Hint: follow the...
(1 point) The nicotine content in cigarettes of a certain brand is normally distributed with mean...
(1 point) The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) u and standard deviation o= 0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5 mg. Now, suppose a reporter wants to test whether the mean nicotine content is actually higher than advertised. He takes measurements from a SRS of 20 cigarettes of this brand. The sample yields an average of 1.55 mg of nicotine. Conduct a test...
(1 point) The nicotine content in cigarettes of a certain brand is normally distributed with mean...
(1 point) The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) u and standard deviation o= 0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5 mg. Now, suppose a reporter wants to test whether the mean nicotine content is actually higher than advertised. He takes measurements from a SRS of 20 cigarettes of this brand. The sample yields an average of 1.4 mg of nicotine. Conduct a test...
Let μ be the true average nicotine content of a brand of cigarettes whose nicotine content...
Let μ be the true average nicotine content of a brand of cigarettes whose nicotine content may reasonably be assumed Normally distributed with σ = 0.2. Suppose the observed sample mean of the nicotine content from 32 randomly selected cigarettes: = 1.4. Find the p-value associated with the following hypothesis: Ho : μ = 1.5 vs. HA : μ 1.5 What do you conclude?
A cigarette manufacturer claims that the average nicotine content of their new brand XXX is at mo...
A cigarette manufacturer claims that the average nicotine content of their new brand XXX is at most 1.35 mg. It would be unwise to reject the manufacturer's claim without strong contradictory evidence. An appropriate problem formulation is to test A random sample of 100 brand XXX cigarettes are tested and the sample standard deviation and sample mean are found to be 0.07 mg and 1.361 mg, respectively. Assuming the central limit theorem applies and s ≈ σ, find the p-value...
The nicotine content in a certain brand of king-size cigarettes has a normal distribution with a...
The nicotine content in a certain brand of king-size cigarettes has a normal distribution with a mean content of 1.8 mg and a standard deviation of 0.2 mg. Find the probability that the nicotine content of a randomly chosen cigarette of this kind is (a) more than 1.95 mg; (b) between 1.95 mg and 2.35 mg.
(2 points) For each problem, select the best response. a) The nicotine content in cigarettes of...
(2 points) For each problem, select the best response. a) The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) u and standard deviation o=0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5, but you believe that the mean nicotine content is actually higher than advertised. To explore this, you test the hypotheses H. :p=1.5, H iu > 1.5 and you obtain a P-value of 0.052. Which of the...
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean...
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.918 g and a standard deviation of 0.304 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. In what range would you expect to find the middle 80% of amounts of nicotine in these cigarettes (assuming the mean has not changed)? (Enter your answers in ascending order...smaller on left, larger on right. Also, enter your...
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean...
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.894 g and a standard deviation of 0.302 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. In what range would you expect to find the middle 60% of amounts of nicotine in these cigarettes (assuming the mean has not changed)? Between and . (Enter your answers in ascending order...smaller on left, larger on right. Also,...
3. The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) 4. The brand advertises that the mean nicotine content of their cigarettes is 1.5, but measurements on a random sample of 100 cigarettes of this brand gave a mean of r = 1.53 and standard deviation s=0.1. Is there sufficient evidence in the sample to suggest that the mean nicotine content is actually higher than advertised? Use a = 0.05. (Hint: follow the...
(1 point) The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) u and standard deviation o= 0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5 mg. Now, suppose a reporter wants to test whether the mean nicotine content is actually higher than advertised. He takes measurements from a SRS of 20 cigarettes of this brand. The sample yields an average of 1.55 mg of nicotine. Conduct a test...
(1 point) The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) u and standard deviation o= 0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5 mg. Now, suppose a reporter wants to test whether the mean nicotine content is actually higher than advertised. He takes measurements from a SRS of 20 cigarettes of this brand. The sample yields an average of 1.4 mg of nicotine. Conduct a test...
Let μ be the true average nicotine content of a brand of cigarettes whose nicotine content may reasonably be assumed Normally distributed with σ = 0.2. Suppose the observed sample mean of the nicotine content from 32 randomly selected cigarettes: = 1.4. Find the p-value associated with the following hypothesis: Ho : μ = 1.5 vs. HA : μ 1.5 What do you conclude?
The nicotine content in a certain brand of king-size cigarettes has a normal distribution with a mean content of 1.8 mg and a standard deviation of 0.2 mg. Find the probability that the nicotine content of a randomly chosen cigarette of this kind is (a) more than 1.95 mg; (b) between 1.95 mg and 2.35 mg.
(2 points) For each problem, select the best response. a) The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) u and standard deviation o=0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5, but you believe that the mean nicotine content is actually higher than advertised. To explore this, you test the hypotheses H. :p=1.5, H iu > 1.5 and you obtain a P-value of 0.052. Which of the...
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