With two COVID-19 vaccines now in the final stages of approval for use in the U.S., 63% of Americans say they are willing to receive a COVID-19 vaccination approved by the Food and Drug Administration (FDA), up from 50% who said this in September. The December results came from a Gallup poll conducted Nov. 16-29, 2020, with a random sample of 2,968 adults. The September results came from a Gallup poll conducted Sept. 14-27, 2020, with a random sample of 2,730 adults. Does this data suggest that the share of Americans who say they plan to get vaccinated has increased? State and test the relevant hypotheses at significance level 0.10 by using the P-value method.
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- What is meant by the sample space of an experiment?A low-level CDC bureaucrat wants to please his boss by gathering evidence that the current government mandated shut down of society is not causing people's mental health to deteriorate, so that it can safely be continued for several years if the expert says is necessary. He pulls a random sample of 1600 citizens, Gathering data on such items as income loss, weight gain, access to toilet paper, our spent binge watching Netflix, and number of injuries caused by household fight, and compiles all this into a significantly-weighted "misery index". The mean misery index from the sample is 99.2; it seems reasonable to use a population standard deviation o=19.1. A. Does this information provide significant evidence (at the 5% level) that the Nationwide mean misery index is less than 100? Set up appropriate null and alternative hypothesis, calculate the appropriate test statistic, find the p-value, and state your conclusion.In the search for a cure for the Coronavirus, it is important to determine what proportion of the population has antibodies, which would likely make them immune or less susceptible to the effects of the disease. According to an article in Politico published on April 26, 2022, 60% of Americans currently have detectible antibodies for Covid-19. A researcher thinks that more than 60% of Americans currently have antibodies for Covid-19. Suppose that the researcher takes a simple randomsample of 1200 Americans, tests their blood, and find that 750 of them have antibodies. Use a 0.05 significance level to test the researcher’s claim.
- A low-level CDC bureaucrat wants to please his boss by gathering evidence thatthe current government-mandated shutdown of society is not causing people’s mentalhealth to deteriorate, so that it can safely be continued for several years if anyexpert says it’s necessary.He polls a random sample of 1600 citizens, gathering data on such items asincome loss, weight gain, access to toilet paper, hours spent binge-watchingNetflix, and number of injuries caused by household fights, and compiles all thisinto a scientifically-weighted “misery index”.The mean misery index from the sample is 99.2; it seems reasonable to use apopulation standard deviation σ = 19.1.a) Does this information provide significant evidence (at the 5% level) that thenationwide mean misery index is less than 100? Set up appropriate null andalternative hypotheses, calculate the appropriate test statistic, find the P-value,and state your conclusion. (10)b) A CDC press release publishing the results of this study claims that…A low-level CDC bureaucrat wants to please his boss by gathering evidence thatthe current government-mandated shutdown of society is not causing people’s mentalhealth to deteriorate, so that it can safely be continued for several years if anyexpert says it’s necessary.He polls a random sample of 1600 citizens, gathering data on such items asincome loss, weight gain, access to toilet paper, hours spent binge-watchingNetflix, and number of injuries caused by household fights, and compiles all thisinto a scientifically-weighted “misery index”.The mean misery index from the sample is 99.2; it seems reasonable to use apopulation standard deviation σ = 19.1.a) Does this information provide significant evidence (at the 5% level) that thenationwide mean misery index is less than 100? Set up appropriate null andalternative hypotheses, calculate the appropriate test statistic, find the P-value,and state your conclusion. b) A CDC press release publishing the results of this study claims that…In a study of the effectiveness of a new device that supports a weak or damaged heart, 150 people who consented to treatment were assigned at random to either a standard treatment consisting of drugs or the experimental treatment that consisted of drugs and surgery to install the new device. After two years, 60% of the 67 patients who received the device had improved and 40% of the patients who received the standard treatment had improved. Does this data provide convincing evidence that the proportion of patients who recieved the experimental treatment who improved is higher than for the patients who received the standard treatment? Test the relevant hypotheses using a significance level of 0.05. (Use pexperimental − pstandard ).A) State the null and alternative hypotheses. H0: pe − ps = 0, HA: pe − ps ≠ 0 H0: pe − ps = 0, HA: pe − ps < 0 H0: pe − ps = 0, HA: pe − ps > 0 B) Find the test statistic.z = C) What is the p-value?P-Value = D) State your conclusion in terms of…
- Patients immobilized for a substantial amount of time can develop deep vein thrombosis (DVT), a blood clot in a leg or pelvis vein. DVT can have serious adverse health effects and can be difficult to diagnose. On its website, drug manufacturer Pfizer reports the outcome of a study looking at the effectiveness of the drug Fragmin (dalteparin) in preventing DVT in immobilized patients. Of the 1518 randomly chosen immobilized patients given Fragmin, 42 experienced a complication from DVT. Of the 1473 randomly chosen immobilized patients given a placebo, 73 experienced a complication from DVT. Compute the proportion (risk) of patients experiencing DVT complications for immobilized patients treated with Fragmin. (Enter the proportion with 4 decimal places. DO NOT enter the percent.)In randomized, double-blind clinical trials of a new vaccine, children were randomly divided into two groups. Subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. After the second dose, 116 of 651 subjects in the experimental group (group 1) experienced fever as a side effect. After the second dose, 73 of 532 of the subjects in the control group (group 2) experienced fever as a side effect. Does the evidence suggest that a higher proportion of subjects in group 1 experienced fever as a side effect than subjects in group 2 at the α=0.10 level of significance? #1 Find the test statistic for this hypothesis test.In randomized, double-blind clinical trials of a new vaccine, infants were randomly divided into two groups. Subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. After the second dose, 126 of 387 subjects in the experimental group (group 1) experienced drowsiness as a side effect. After the second dose, 158 of 574 of the subjects in the control group (group 2) experienced drowsiness as a side effect. Does the evidence suggest that a higher proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the α=0.01 level of significance? Verify the model requirements. Select all that apply. A. The sample size is less than 5% of the population size for each sample. B. n1p11−p1≥10 and n2p21−p2≥10 C. The samples are dependent. D. The sample size is more than 5% of the population size for each sample. E. The samples are independent. F. The data come…
- A consumer advocacy group wanted to study whether different airline carriers differed in terms of their delayed flights. In particular, the researchers were interested in the relationship between p1, the proportion of Alpha Airlines flights that were delayed at least 15 minutes, and p2, the proportion of Beta Airlines flights that were delayed at least 15 minutes. A random sample of 1,000 Alpha flights and a separate random sample of 1,000 Beta flights found that 67 of the Alpha fights and 160 of the Beta flights were delayed at least 15 minutes. The conditions for inference were checked and verified. Does this set of samples provide strong evidence that Alpha Airlines has a smaller proportion of flights that are delayed at least 15 minutes than Beta Airlines, at the α = 0.05 significance level? Find the z-table here. A. The test statistic is z = –6.56 and the P-value ≈ 0. Since the P-value ≈ 0 < 0.05, there is not sufficient evidence that Alpha Airlines has fewer delayed…The manufacturer of a new racecar engine claims that the proportion of engine failures due to overheating for this new engine, (p1)(p1), will be no higher than the proportion of engine failures due to overheating of the old engines, (p2)(p2). To test this statement, NASCAR took a random sample of 165165 of the new racecar engines and 145145 of the old engines. They found that 1818 of the new racecar engines and 1212 of the old engines failed due to overheating during the test. Does NASCAR have enough evidence to reject the manufacturer's claim about the new racecar engine? Use a significance level of α=0.01α=0.01 for the test. Step 1 of 6 : State the null and alternative hypotheses for the test. Step 2 of 6: Find the vales of the two sample proportions P1 and P2.Round your answers three decimal places. Step 3 of 6: Compute the weighted estimate p. p(line above). Round your answers to three decimal places. Step 4 of 6: Compute the value of the test statistic. Round your answer to two…A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Though the two brands have been comparable in the past, some technological advances were recently made in the Brand 2 manufacturing process, and the consumer group is testing to see if Brand 2 will outperform Brand 1. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 12 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in Table 1. Car Brand 1 Brand 2 Difference(Brand 1 - Brand 2) 1 0.366 0.319 0.047 2 0.364 0.307 0.057 3 0.316 0.359 -0.043 4 0.277 0.298 -0.021 5…