3.) In a particular epidemic disease, 400 individuals were surveyed by a well-established pharmaceutical company to determine if the company’s new vaccine was effective after 4 months. Among the 120 individuals who had that disease and were given the shot, 29 were cured and achieved immunity after 4 months. Among 280 individuals who had the disease but were not given the shot, 56 were cured and achieved immunity after 4 months. Is there enough statistical evidence to support the company’s claim of the effectiveness of the vaccine?
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- A clinical trial is conducted to compare an experimental medication to placebo to reduce the symptoms of asthma. Two hundred participants are enrolled in the study and randomized to receive either the experimental medication or placebo. The primary outcome is self-reported reduction of symptoms. Among 100 participants who receive the experimental medication, 38 report a reduction of symptoms as compared to 21 participants of 100 assigned to placebo. When you test if there is a significant difference in the proportions of participants reporting a reduction of symptoms between the experimental and placebo groups. Use α = 0.05. What should the researcher’s conclusion be for a 5% significance level? Reject H0because 2.64 ≥ 1.960. We have statistically significant evidence at α = 0.05 to show that there is a difference in the proportions of patients reporting a reduction in symptoms. We reject H0 at the 5% level because 2.64 is greater than 1.96. We do have statistically…researcher suspects that the actual prevalence of generalized anxiety among children and adolescents is higher than the previously reported prevalence of generalized anxiety disorder among children and adolescents. The previously reported prevalence of generalized anxiety disorder among children and adolescents is 3.9%, and the researcher conducts a study to test the accuracy of the previously reported prevalence of generalized anxiety disorder by recruiting 98 children and adolescents from various pediatricians' offices and tests them for generalized anxiety disorder using the DSM-5. The researcher determines that the prevalence of generalized anxiety disorder among the participants of the study is 6.1%. What should the researcher's conclusion be for a 5% significance level? A. We reject H0 at the 5% level because -57.53 is less than -1.96. We do have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents…An experimenter has prepared a drug-dose level that he claims will induce sleep for at least 70% of people suffering from insomnia. After examining the dosage we feel that his claims regarding the effectiveness of his dosage are too high. In an attempt to disprove his claim, we administer his prescribed dosage to 80 insomniacs and observe that 51 of them have had sleep induced by the drug dose. Is there enough evidence to refute his claim at the 5% level of significance? a) state null and alternate hypotheses b) find the test statistic and rejection region c) state your conclusion
- Angioplasty is a medical procedure in which an obstructed blood vessel is widened. In some cases, a wire mesh tube, called a stent, is placed in the vessel to help it remain open. A study was conducted to compare the effectiveness of a bare metal stent with one that has been coated with a drug designed to prevent reblocking of the vessel. A total of 5329 patients received bare metal stents, and of these, 830 needed treatment for reblocking within a year. A total of 1125 received drug-coated stents, and 146 of them required treatment within a year. Can you conclude that the proportion of patients who needed retreatment differs between those who received bare metal stents and those who received drug-coated stents? Let p1 denote the proportion of patients with bare metal stents who needed retreatment and p2 denote the proportion of patients with drug-coated stents who needed retreatment. Use the α=0.10 level of significance and the P-value method with the TI-84 Plus calculator. a)State…A doctor is studying the relationship between blood pressure and heartbeat abnormalities in her patients. She tests a random sample of her patients and notes their blood pressures (high, low, or normal) and their heartbeats (regular or irregular). She finds that: 14% have high blood pressure. • 22% have low blood pressure. 15% have an irregular heartbeat. • Of those with an irregular heartbeat, one-third have high blood pressure. • Of those with normal blood pressure, one-eighth have an irregular heartbeat. What portion of the patients selected have a regular heartbeat and low blood pressure? (0.2)Independent studies show that 26 out of 40 r/s full-time students favor a shorter semester system, while 38 out of 50 r/s part-time students favor the same. Construct a 98% c.i. for the difference between the overall percentage of full-time students favoring a shorter semester system and that of part-time students.
- A researcher took a random sample of 200 new mothers in the United States (Group 1) and found that 16% of them experienced some form of postpartum depression. Another random sample of 200 new mothers in France (Group 2), where mothers receive 16 weeks of paid maternity leave, found that 11% experienced some form of postpartum depression. Can it be concluded that the percent of women in the United States experience more postpartum depression than the percent of women in France? Use α=0.05. Select the correct alternative hypothesis and decisionA 2012 survey of 417 American adults indicates that 15% of cell phone owners do their browsing on their phone rather than a computer or other device. According to an online article, a report from a mobile research company indicates that 38% of Chinese mobile web users only access the internet through their cell phones. We wish to conduct a hypothesis test to determine if these data provide strong evidence that the proportion of Americans who only use their cell phones to access the internet is less than the Chinese proportion of 38%. (a) The Null Hypothesis, in mathematical symbols, is: H0: p = ______ (b) The Alternative Hypothesis, in mathematical symbols, is: HA : p = _______ In both the null and alternative hypotheses, the symbol ( p ) is the proportion of American adult cell phone owners who do their browsing on their phone. (c) The standard error based on the null hypothesis is... :________ (d) Our data indicates a proportion of Americans who use their phones to browse is…It has been hypothesized that allergies result from a lack of early childhood exposure to antigens. If this hypothesis were true, then we would expect allergies to be more common in very hygienic households with low levels of bacteria and other infectious agents. To test this theory, researchers at the University of Colorado sampled the houses of 61 children 9-24 months old and recorded two variables: (1) whether the child tested positive for allergies and (2) the concentration of bacterial endotoxin in the house dust (endotoxin units per ml, EU/ml)1. The following are the endotoxin levels at the homes of the 51 children tested negative for allergies. 708.23 911.60 976.81 1316.63 262.74 9772.08 370.76 229.16 2570.51891.19 3163.20 1777.65 1288.57 436.23 2631.63 1173.52 911.67 7942.42 740.32 356.92 1175.48 1480.55 2754.61 575.62 573.89 468.26 1000.71 364.22 1025.26 1022.04 645.41 363.57 977.47 1022.75 1860.63 371.13 174.73 399.68 1479.77 2882.96…
- The Substance Abuse and Mental Health Services Administration (SAMHSA, 2017) estimates that 10.9% of the population of the United States age 18–24 had an episode of depression in the previous 12 months. Suppose a researcher takes a random sample of 225 United States adults aged 18–24. Determine the value of the sample proportion, p, such that 5% of samples of 225 United States adults age 18–24 are greater than p. You may find software or a z-table useful. Give your answer precise to three decimal places. p = IIA researcher is studying a new treatment protocol to combat a certain disease. The interest is in comparing the performance of the new treatment with the standard treatment method. In a survey on the subject, a first group of 250 patients received standard treatment, while a second group of 185 patients received the new treatment. Among subjects treated with the standard method, 88 were not recovered, while 39 were not recovered among those treated with the new protocol. Statistical analysis should be done to evaluate and compare treatment options. Perform an appropriate statistical hypothesis test to see whether the rate of people with disease persistence (ie, the non-recovery rate) was lower among those who received the new treatment. The hypothesis test must use a significance level of α=0.09 a. What is the value of the test statistic? b. What range of values is the p-value in? c. At the 9% significance level, can the null hypothesis be rejected?An experiment to evaluate the effectiveness of the type of snack and children's perception of satiation was designed so that subjects aged 10 to 13 years were randomly assigned a snack that was of the exact same ingredients but described differently. The first group had their snack described as healthy and full of vitamins, the second group had their snack described as tasty, the third group were given a snack without any description whatsoever. Thirty minutes after finishing the snack, subjects were asked to rate their hunger on a scale of 1 to 10. The results are summarized in the table: ANOVA: Single Factor SUMMARY Groups Healthy Tasty No Description ANOVA Source of Variation Between Groups Within Groups Total Count 12 13. 14 SS 17.46154 62.89744 80.35897 Sum 62 46 56 Average 5.1667 3.5385 4.0000 Variance 1.9697 1.9359 1.3846 df MS F P-value 2 8.730769 4.997146 0.012156 36 1.747151 38 Based on these results, at a 5% level of significance what conclusion can the researchers draw from…
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