The virus COVID-19 is currently a pressing local and global concern, and a new bivalent vaccine dose becoming more widely available. Living in a university town, a researcher wonders what proportion of adults in Benton County have the most recent bivalent vaccine dose for COVID-19. To examine this, the researcher takes a random sample of 300 residents in Benton County and discovers that 61 of those individuals have received the bivalent vaccine dose. What proportion of Benton County residents have gotten the bivalent vaccine dose for a. b. C. d. COVID-19? Check the sample size conditions for using z-procedures to construct a confidence interval for p. Explain whether these size conditions are met. Estimate the proportion of Benton County residents who have gotten the bivalent vaccine dose for COVID-19. Use a confidence level of 95%. (Calculate the 95% confidence interval) Show setup/work and give answer in interval notation, rounded to four places past the decimal. Interpret your point/interval estimate for p. That is, provide the two-part conclusion for your confidence interval, including context.
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- Each year, over 2 million people in the United States become infected with bacteria that are resistant to antibiotics. In particular, the Centers of Disease Control and Prevention has launched studies of drug-resistant gonorrhea (CDC.gov website). Of 142 cases tested in Alabama, 9 were found to be drug-resistant. Of 268 cases tested in Texas, 5 were found to be drug-resistant. Do these data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states? Use a 0.02 level of significance. What is the p-value, and what is your conclusion? Test statistic = (to 2 decimals) p-value = (to 4 decimals) Conclusion: Select your answer - Choose the correct option. There is a significant difference in drug resistance between the two states. Alabama has the higher drug resistance rate. - Select your answer - ▼The impact of a low-calorie diet on laboratory mice's longevity is being investigated by a medical researcher. Twenty mice are split into two groups (E and F) by random. A typical diet is given to Group E, while Group F is given a diet that only contains 70% as many calories as Group E's diet. The length of life (in days) of each mouse over the 36-month trial is documented. Table 2 provides the data that was obtained. The symbol of double star (**) signifies that the mouse was still alive at the end of the investigation. (a) (b) (c) Table 2: The length of life (in days) of each mouse Group E 900 907 751 833 920 787 830 877 848 901 Group F 1037 905 1023 988 1078 1011 ** 1063 898 1033 State a suitable null and alternative hypotheses for the problem. At 5% significance level, test the hypotheses in part (a) by using an appropriate nonparametric test. Write your conclusion.The Virginia Department of Health publishes COVID-19 vaccination data on their website. As of 10/5/2021, 60.6% of the population of Virginia is fully vaccinated. This rate varies drastically from county to county. Specifically, Fairfax County’s full vaccination rate is 74% and Lee County’s full vaccination rate is 40%. A researcher took a random sample of 14 individuals from Fairfax County and another random sample of 14 individuals from Lee County and asked them whether they could verify that they are fully vaccinated. Each sample was selected in a single day. 1. Calculate the mean and standard deviation of the number of individuals from Fairfax County and Lee County in this sample who are fully vaccinated. Show your work using the binomial mean and binomial standard deviation formulas and provide your two means and two standard deviations in your document. Round your answers to two decimal places. (It is not necessary to use StatCrunch for this part.) 2. Calculate the probability…
- Most cases of cervical cancer are linked to a few strains of the human papilloma virus (HPV). The pharmaceutical company Merck developed a vaccine (Gardisil) against these HPV strains. Worldwide clinical trials followed young women after vaccination or administration of placebo for two to four years for signs of HPV-caused cervical cancer. Based on a sample of 100 women in the Gardisil group, 34 % developed cervical cancer, and based on a sample of 100 women in the placebo group, 44 % developed cervical cancer. Test the claim that the proportion of women who developed cervical cancer in the Gardisil group is less than the proportion of women who developed cervical cancer in the placebo group at a = 0.05. Round your answers to three decimal places, and round any interim calculations to four decimal places. Fill in the hypotheses below where p₁ denotes the proportion of women who developed cervical cancer in the Gardisil group and p2 denotes the proportion of women who developed cervical…Most cases of cervical cancer are linked to a few strains of the human papilloma virus (HPV). The pharmaceutical company Merck developed a vaccine (Gardisil) against these HPV strains. Worldwide clinical trials followed young women after vaccination or administration of placebo for two to four years for signs of HPV-caused cervical cancer. Based on a sample of 100 women in the Gardisil group, 24 % developed cervical cancer, and based on a sample of 100 women in the placebo group, 34 % developed cervical cancer. Test the claim that the proportion of women who developed cervical cancer in the Gardisil group is less than the proportion of women who developed cervical cancer in the placebo group at a = 0.10. Round your answers to three decimal places, and round any interim calculations to four decimal places. Fill in the hypotheses below where p₁ denotes the proportion of women who developed cervical cancer in the Gardisil group and P2 denotes the proportion of women who developed cervical…Most cases of cervical cancer are linked to a few strains of the human papilloma virus (HPV). The pharmaceutical company Merck developed a vaccine (Gardisil) against these HPV strains. Worldwide clinical trials followed young women after vaccination or administration of placebo for two to four years for signs of HPV-caused cervical cancer. Based on a sample of 100 women in the Gardisil group, 34 % developed cervical cancer, and based on a sample of 100 women in the placebo group, 44% developed cervical cancer. Test the claim that the proportion of women who developed cervical cancer in the Gardisil group is less than the proportion of women who developed cervical cancer in the placebo group at a = 0.05. Round your answers to three decimal places, and round any interim calculations to four decimal places. Fill in the hypotheses below where p₁ denotes the proportion of women who developed cervical cancer in the Gardisil group and p2 denotes the proportion of women who developed cervical…
- Most cases of cervical cancer are linked to a few strains of the human papilloma virus (HPV). The pharmaceutical company Merck developed a vaccine (Gardisil) against these HPV strains. Worldwide clinical trials followed young women after vaccination or administration of placebo for two to four years for signs of HPV-caused cervical cancer. Based on a sample of 100 women in the Gardisil group, 26% developed cervical cancer, and based on a sample 100 women in the placebo group, 32% developed cervical cancer. Test the claim that the proportion of women who developed cervical cancer in the Gardisil group is less than the proportion of women who developed cervical cancer in the placebo group at a = 0.05. Round your answers to three decimal places, and round any interim calculations to four decimal places. Fill in the hypotheses below where p₁ denotes the proportion of women who developed cervical cancer in the Gardisil group and p2 denotes the proportion of women who developed cervical…Most cases of cervical cancer are linked to a few strains of the human papilloma virus (HPV). The pharmaceutical company Merck developed a vaccine (Gardisil) against these HPV strains. Worldwide clinical trials followed young women after vaccination or administration of placebo for two to four years for signs of HPV-caused cervical cancer. Based on a sample of 100 women in the Gardisil group, 24 % developed cervical cancer, and based on a sample of 100 women in the placebo group, 34 % developed cervical cancer. Test the claim that the proportion of women who developed cervical cancer in the Gardisil group is less than the proportion of women who developed cervical cancer in the placebo group at a = 0.10. Round your answers to three decimal places, and round any interim calculations to four decimal places. Fill in the hypotheses below where p₁ denotes the proportion of women who developed cervical cancer in the Gardisil group and p2 denotes the proportion of women who developed cervical…Most cases of cervical cancer are linked to a few strains of the human papilloma virus (HPV). The pharmaceutical company Merck developed a vaccine (Gardisil) against these HPV strains. Worldwide clinical trials followed young women after vaccination or administration of placebo for two to four years for signs of HPV-caused cervical cancer. Based on a sample of 100 women in the Gardisil group, 26% developed cervical cancer, and based on a sample of 100 women in the placebo group, 32% developed cervical cancer. Test the claim that the proportion of women who developed cervical cancer in the Gardisil group is less than the proportion of women who developed cervical cancer in the placebo group at a = 0.05. Round your answers to three decimal places, and round any interim calculations to four decimal places. Fill in the hypotheses below where p₁ denotes the proportion of women who developed cervical cancer in the Gardisil group and p2 denotes the proportion of women who developed cervical…
- Although arsenic is known to be a poison, it also has some beneficial medicinal uses. In one study of the use of arsenic to treat acute promyelocytic leukemia (APL), a rare type if blood cancer, APL patients were given an arsenic compound as part of their treatment. Of those receiving arsenic, 32% were in remission and showed no signs of leukemia in subsequent examination. It is known that 18% of APL patients go into remission after conventional treatment. Suppose that the study had included 100 randomly selected patients. Is there sufficient evidence to conclude that the proportion in remission for the arsenic treatment is greater than 0.18, the remission proportion for conventional treatment? a. Test the hypothesis at the 0.01 significance level. b. Construct and interpret a 99% confidence interval for the true proportion of APL patients who go into remission after using arsenic. Does the inference drawn from this interval match the conclusion from the test that you did in part…An independent research group has been studying the chances that an accident at a nuclear power plant will result in radiation leakage. The group considers that the only possible types of accidents at a reactor are fire, mechanical failure, and human error, and that two or more accidents never occur together. It has performed studies that indicate that if there were a fire, a radiation leak would occur 20 percent of the time; if there were a mechanical failure, a radiation leak would occur 50 percent of the time; and if there were a human error, a radiation leak would occur 10 percent of the time. Its studies have also shown that the probability of A fire and a radiation leak occurring together is 0.0010. A mechanical failure and a radiation leak occurring together is 0.0015. A human error and a radiation leak occurring together is 0.0012. (a)What are the respective probabilities of a fire, mechanical failure, and human error? (b)What are the respective probabilities that a…Most cases of cervical cancer are linked to a few strains of the human papilloma virus (HPV). The pharmaceutical company Merck developed a vaccine (Gardisil) against these HPV strains. Worldwide clinical trials followed young women after vaccination or administration of placebo for two to four years for signs of HPV-caused cervical cancer. Based on a sample of 100 women in the Gardisil group, 26% developed cervical cancer, and based on a sample of 100 women in the placebo group, 32% developed cervical cancer. Test the claim that the proportion of women who developed cervical cancer in the Gardisil group is less than the proportion of women who developed cervical cancer in the placebo group at a = 0.05. Round your answers to three decimal places, and round any interim calculations to four decimal places. Fill in the hypotheses below where p₁ denotes the proportion of women who developed cervical cancer in the Gardisil group and p2 denotes the proportion of women who developed cervical…