In a large clinical trial, 395,409 children were randomly assigned to two groups. The treatment group consisted of 196,674 children given a vaccine for a certain disease, and 36 of those children developed the disease. The other 198,735 children were given a placebo, and 113 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Complete parts (a) through (d) below. ..... a. Assume that a 0.05 significance level will be used to test the claim that p1
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![In a large clinical trial, 395,409 children were randomly assigned to two groups. The treatment group consisted of 196,674 children given a vaccine for a certain disease, and 36 of those children developed the disease. The other 198,735 children were given a placebo, and 113 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Complete parts (a) through (d) below.
a. Assume that a 0.05 significance level will be used to test the claim that \( p_1 < p_2 \). Which is better: A hypothesis test or a confidence interval?
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- In a study, a large sample representative of the households in the US were asked about their smoking habits. The data suggested that current smokers were on average much healthier than those who recently stopped smoking. Investigators concluded that smoking does not necessarily lead to worse health outcomes. Consider the following statements. Select the ones you agree with, based on the information given. Group of answer choices A.In a randomized experiment, smoker and non-smoker groups are similar across all potential characteristics. b.The conclusions were justified by the data. c.This is an observational study. d.This study is a randomized controlled experiment. e.The results can be explained due to confounding. Current smokers are different from those who recently stopped in ways that are related to health outcomes.13) A group of medical researchers are developing a treatment program that is intended to reduce blood pressure levels of patients who are at risk of heart diseases. They have selected a random sample of 12 patients and measured their systolic blood pressure levels. Then they were given the treatment for 4 weeks and remeasured the systolic blood pressure levels. The observations before and after the treatment program are shown below: Patient 1 2 3 4 5 6 7 8 9 10 11 12 Before 145 134 155 140 138 150 148 152 129 142 149 137 After 134 132 145 143 134 146 134 150 125 138 140 132 Use 5% significance level to test the claim that the treatment program lowers the systolic blood pressure level on average. a) What are the null and alternative hypotheses for this test? b) What are the mean differences (before - after) and the standard deviation of differences for this sample of 12 patients? Give two decimal…A report describes a survey of 500 licensed drivers. Each driver in the sample was asked if they would prefer to keep complete control of the car while driving, to use a partially self-driving car that allowed partial driver control, or to turn full control over to a driverless car. Suppose that it is reasonable to regard this sample as a random sample of licensed drivers in the United States, and that you want to use the data from this survey to decide if there is evidence that fewer than half of all licensed drivers in the United States prefer to keep complete control of the car while driving. (d) The actual sample proportion observed in the study was p̂ = 0.44. Based on this sample proportion, is there convincing evidence that fewer than 50% of licensed drivers prefer to keep complete control of the car when driving, or is the sample proportion consistent with what you would expect to see when the null hypothesis is true? Support your answer with a probability calculation. (Round…
- A researcher is conducting an experimental study on the effect of aspirin on heart attack risk. In order to assign who will receive aspirin and who will receive a placebo, she first divides her study into three age groups (18-29, 30-49, and 50 or older). She then randomly assigns individuals within these age groups to either receive aspirin or the placebo. This is an example of a cluster ?A sociologist studying New York City ethnic groups wants to determine if there is a difference in income for immigrants from four different countries during their first year in the city. She obtained the data in the following table from a random sample of immigrants from these countries (incomes in thousands of dollars). Use a 0.05 level of significance to test the claim that there is no difference in the earnings of immigrants from the four different countries. 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The dotplot shows the proportion who would go to the professor in each of 1000 random samples of size 172 from a population where 11% would go to the professor. 17 0.1 0.15 0.2 0.25 Simulated sample proportion who would say "Yes" 0 0.05 Distribution of simulated proportion # samples 1000 mean 0.11 SD 0.024 (a) Use the results of the simulation to approximate the margin of error for Gallup's estimate of the proportion of U.S. adults who were satisfied with the way things were going in the United States at the time of the poll. (b) Interpret the margin of error.A pharmaceutical company is testing the effectiveness of its vaccine across two different age brackets. They take a sample and split the participants up into two separate groups. Group A consists of 44 people who are between ages 13 and 18. Group B consists of 58 people between ages 19 and 26. After being administered the vaccine, it was found that 37 people from group A were immune to the virus and 42 people from group B were immune. What proportion of people from Group A were immune? What proportion of people from Group B were immune? What proportion of people in this study were immune?A random survey of health issues, conducted by the Department of Public Health of the Commonwealth of Massachusetts, examined the results from the state's seven largest cities. These cities were selected on the basis of their diverse racial and ethnic populations. The percentage of adults with diabetes in each city in the survey is given in the following table. City Boston Worcester Springfield Lowell Fall River Lawrence NewBedford Adults withDiabetes (%) 4.2 5.2 9.1 5.7 8.1 7.9 6.3 Find the average percentage of adults with diabetes in these seven cities. (Round your answer to two decimal places.) %What is the standard deviation for these data? 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