3) A certain country claims that their COVID-19 vaccine is more than 80% effective. In their clinical trial test, 810 out of 1000 subjects received protection and prevented them from the virus infection. a) For a one-tailed test, what should be the hypotheses? b) What is the t-value/ z-value?
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- A researcher surveyed 500 people. She found that the individuals who took some form of over the counter sleep aid (i.e. ZZZQuil) were able to fall asleep in a shorter period of time and stay asleep for longer periods than the individuals who did not. a) Was this study observational or experimental? Why?b) What was the explanatory variable? What was the response variable?Echinacea is widely used as an herbal remedy for the common cold, but does it work? In a double-blind experiment, healthy volunteers agreed to be exposed to common-cold-causing rhinovirus type 39 and have their symptoms monitored. The volunteers were randomly assigned to take either a placebo or an echinacea supplement daily for 5 days following viral exposure. Among the 103 subjects taking a placebo, 88 developed a cold, whereas 44 of the 48 subjects taking echinacea 1 developed a cold.A comprehensive trial investigating the relationship between vitamin E supplementation and reduced risk for prostate cancer was carried out across the US. Suppose the trial reported that among the 648 patients receiving the supplement program, 267 developed prostate cancer, while only 212 of the 711 patients without the supplementation developed the disease. Carry out a formal test to determine if there is a significant difference in the risk for developing prostate cancer among the two groups. Write out your null and alternative hypotheses and use an alpha level of 0.05. Also, Comment on the effectiveness of the supplementation at reducing prostate cancer. What did you find relevant to the research hypothesis?
- In randomized, double-blind olinical trials of a new vaccine, rats were randomly divided into two groups. Subjects in group x received the new vaccine while subjects in group y received a control vaccine. After the first dose, 118 of 718 subjects in the experimental group (group x) experienced vamiting as a side effect. After the first dose, 74 of 619 of the subjects in the control group (group y) experienced vomiting as a side effect. Construct a 95% confidence interval for the difference between the two population proportions, P, - P, The 95% confidence interval for P,-P, is ( (Round to three decimal places as needed.)A researcher wants to test the effectiveness of a new drug to treat asthma. One hundred patients with chronic, stable asthma were randomly assigned to one of three groups to receive a placebo (0mg), 1mg of drug, or 5 mg of drug. After treatment, a doctor tested the patient’s forced expiratory volume for 1 second (FEV1). Which statistical test would be best to determine if there is a significant difference between groups?A mutation in Gene A is thought to be associated with a disease. The mutation in Gene A is found in 5% of the population. 2% of the whole population is diagnosed with disease B at some point in their life time. 1% of the population both has the mutation and also gets diagnosed with the disease in their life time. Is the provided data adequate to test the independency of mutation in Gene A and occurrence of Disease B? If it is not, what other information or data is needed to test the independency? What is the probability of Disease B, among the individuals with the mutation in Gene A? What is the probability of having the mutation in Gene A among the individuals with Disease B? If an individual has the mutated Gene A, what is their Relative Risk of developing the disease?
- A genetic theory says that a cross between two pink flowering plants will produce red flowering plants 25% of the time. To test the theory, 100 crosses are made and 37 of them produce a red flowering plant. Is this strong evidence that the theory is wrong? Carry out the appropriate hypothesis test at the 5% significance level.The appropriate hypothesis for this test is H0: x = 0.25 vs. HA: x ≠ 0.25H0: μ = 0.25 vs. HA: μ ≠ 0.25 H0: p̂ = 0.25 vs. HA: p̂ ≠ 0.25H0: p = 0.25 vs. HA: p ≠ 0.25 The test statistic is (to two places after decimal)the p-value is (to three places after decimal)There enough statistical evidence to conclude that the theory is wrong.Choose the correct hypotheses to test two matched study samples where measures are taken serially in time or under different experimental conditions such as measurements before and after a health intervention. O HO: p1 = p10, p2 = p20,.pk = pk0 H1: H0 is false (where p = proportion of participants in a specific category) O HO: m1 = m2 H1: m1 > m2, m1p2, p1< p2, p1 + p2 O HO: m1 = m2 = m3... = mk H1: Means are not all equal (m = mean) %3DAccording to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.33. Suppose a random sample of 109 traffic fatalities in a certain region results in 45 that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the a= 0.01 level of significance? Because npo (1-Po) ▼satisfied. (Round to one decimal place as needed.) 10, the sample size is 5% of the population size, and the sample the requirements for testing the hypothesis
- According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.33. Suppose a random sample of 107 traffic fatalities in a certain region results in 46 that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the a= 0.01 level of significance? Because npo (1- Po) V10, the sample size is V 5% of the population size, and the sample V the requirements for testing the hypothesis V satisfied. (Round to one decimal place as needed.)According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.35. Suppose a random sample of 106 traffic fatalities in a certain region results in 50 that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the a = 0.01 level of significance? Because npo (1- Po) 10, the sample size is 5% of the population size, and the sample the requirements for testing the hypothesis satisfied. (Round to one decimal place as needed.)A clinical trial is being conducted to determine the efficacy of a novel antiretroviral medication for HIV patients. Patients are randomized to receive either standard antiretroviral therapy or the novel antiretroviral therapy and are followed for three months. The viral load, or the amount of HIV copies per milliliter of blood, is the most important outcome. Is there statistical evidence of a difference in viral load in patients receiving standard versus new anti-retroviral therapy? A total of 30 participants are randomized, and the data are shown below and it is Two tailed Test
