In Exercises 33–36, identify which of these designs is most appropriate for the given experiment: completely randomized design, randomized block design, or matched pairs design. Lunesta Lunesta is a drug designed to treat insomnia. In a clinical trial of Lunesta, amounts of sleep each night are measured before and after subjects have been treated with the drug.
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Q: Migraine and Acupuncture: A migraine is a particularly painful type of headache, which patients…
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In Exercises 33–36, identify which of these designs is most appropriate for the given experiment: completely randomized design, randomized block design, or matched pairs design.
Lunesta Lunesta is a drug designed to treat insomnia. In a clinical trial of Lunesta, amounts of sleep each night are measured before and after subjects have been treated with the drug.
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- Migraine and Acupuncture: A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 164 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 73 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 91 patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below. Test to see if migraine pain relief is dependent on receiving acupuncture. Use α = 0.1. Pain Free: Yes Pain Free: No Total Treatment 20 53 73 Control 6 85 91 Total 26 138 164 a) What is the correct null hypothesis? H0: Migraine pain relief is dependent on…For a statistic to be a good estimator of a parameter, two properties it must satisfy are unbiasedness and minimum variance. Consider a sample of three observations X₁, X₂, X, where X, ~ Exp (0). That is, a sample of size 3 is taken from a population 2 3 following the exponential distribution with density function given by f(x) = 1e % if x > 0 0, Otherwise. Five possible estimators of are â‚ =X₁, Ô₂ = ¹/(X₁ + X₂), Ô‚ = =— (X₁ + 2X₂), Ô¸ = X, and Ô¸ = ¹⁄ (X₂ + X). 2 [Hint: Use the fact that for variable X we have E(X)= 0 and E(X²)=20² and Var(X) = 0². (a) Show that the five estimators given above are unbiased for 0. (b) Find the variances of each of the five estimators. (c) Which estimator will you choose for 0. Why?Migraine and Acupuncture: A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 155 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 79 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 76 patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below. Test to see if migraine pain relief is dependent on receiving acupuncture. Use a = 0.05. Treatment Control Total ∞º Pain Free: Yes Pain Free: No 20 6 26 a) What is the correct null hypothesis? O Ho: Migraine pain relief is dependent on receiving acupuncture. O Ho: P1 = P2 = P3…
- Migraine and Acupuncture: A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 169 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 66 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 103 patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below. Test to see if migraine pain relief is dependent on receiving acupuncture. Use a = .05. Pain Free: Pain Free: Total Yes No Treatment 16 50 66 Control 9 94 103 Total 25 144 169Migraine and Acupuncture: A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 164 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 70 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 94 patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below. Test to see if migraine pain relief is dependent on receiving acupuncture. Use a = 0.05. Pain Free: Yes Pain Free: No Total Treatment Control Total 19 51 70 9 85 94 28 136 164 a) What is the correct null hypothesis? O Ho: P1 P2 P3 = P4 O Ho: Migraine pain relief is dependent on…Researchers are investigating whether people who exercise with a training partner have a greater increase, on average, in targeted exercise intensity compared with people who exercise alone. Two methods of collecting data have been proposed. Method I: Recruit volunteers who are willing to participate. Randomly assign each participant to exercise with a training partner or to exercise alone. Method II: Select a random sample of people from all the people who exercise at a community fitness center. Ask each person in the sample whether they use a training partner, and use the response to create the two groups. (a) For each method, the researchers will record the change in targeted exercise intensity for each person in the investigation. They will compare the mean change in intensity between those who exercise with a training partner and those who do not. (i) Describe the population of generalization if method I is used. Explain your answer. (ii) Describe the population of…
- High levels of cholesterol in the blood are associated with higher risk of heart attacks. Will using a drug to lower blood cholesterol reduce heart attacks? The Helsinki Heart Study recruited middle-aged men with high cholesterol but no history of other serious medical problems to investigate this question. The volunteer subjects were assigned at random to one of two treatments: 2051 men took the drug gemfibrozil to reduce their cholesterol levels, and a control group of 2030 men took a placebo. During the next five years, 56 men in the gemfibrozil group and 84 men in the placebo group had heart attacks. Is the apparent benefit of gemfibrozil statistically significant? Using the p-value that you get from your previous z-test statistic, would you conclude that gemfibrozil is probably effective?Migraine and Acupuncture: A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 161 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 65 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 96 patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below. Test to see if migraine pain relief is dependent on receiving acupuncture. Use αα = 0.05. Pain Free: Yes Pain Free: No Total Treatment 13 52 65 Control 5 91 96 Total 18 143 161 b) Fill in the expected values, round answers to at least 4 decimal places.…The Salk vaccine against polio was tested in 1954 in a carefully designed field experiment. Approximately, 400,000 children took part in this experiment. Using a randomization procedure, the children were randomly divided into 2 groups of equal size, a treatment group, and a control group. The vaccine was given only to the children in the treatment group; the control group children received placebo injections. The children did not know which of the two groups they had been placed into. The diagnosticians also lacked this information. 57 children in the treatment group went on to contract polio, while 142 children in the control group contracted the illness. How likely would such a difference in outcomes be when the assignment to the treatment or control group had absolutely no effect on the outcomes?
- High levels of cholesterol in the blood are associated with higher risk of heart attacks. Will using a drug to lower blood cholesterol reduce heart attacks? The Helsinki Heart Study recruited middle-aged men with high cholesterol but no history of other serious medical problems to investigate this question. The volunteer subjects were assigned at random to one of two treatments: 2051 men took the drug gemfibrozil to reduce their cholesterol levels, and a control group of 2030 men took a placebo. During the next five years, 56 men in the gemfibrozil group and 84 men in the placebo group had heart attacks. Is the apparent benefit of gemfibrozil statistically significant? Using proportion values rounded to four decimal places, what is the z- test statistic? Round your answer to two decimal places.Migraine and Acupuncture: A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control.Patients in the treatment group received acupuncture that is specifically designed to treat migraines and patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below. Test to see if migraine pain relief is dependent on receiving acupuncture. Test at the 8% level and round expected values to one decimal place. Pain Relief Yes (Observed) Yes (Expected Value) No (Observed) No (Expected Value) Row Total No Relief 29 29 58 Control 91 103…Migraine and Acupuncture: A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 152 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 64 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 88 patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below. Test to see if migraine pain relief is dependent on receiving acupuncture. Use α = 0.1. Pain Free: Yes Pain Free: No Total Treatment 16 48 64 Control 6 82 88 Total 22 130 152 b) Fill in the expected values, round answers to at least 2 decimal places. Expected…
