Chapter 11: Q.11.5 (page 459)
Regarding a sample proportion:
a. What is it?
b. What symbol is used for it?
(a) The sample proportion is the percentage of the sample obtained from the proportion.
(b) The symbol for sample proportion is
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Asthmatics and Sulfites. In the article "Explaining au Unusual Allergy, " appearing on the Everyday Health Network, Dr. A. Feldweg explained that allergy to sulfites is usually seen in patients with asthma. The typical reaction is a sudden increase in asthma symptoms after eating a food containing sulfites. Studies are performed to estimate the percentage of the nation's million asthmatics who are allergic to sulfites. In one survey, of randomly selected U.S. asthmatics were found to be allergic to sulfites. Find and interpret a confidence interval for the proportion, , of all U.S. asthmatics who are allergic to sulfites.
Social Networking. A Pew Internet de American Life Project examined Internet social networking. Among a sample of online adults years old, said they use social networking sites. Determine a confidence interval for the percentage of all online adults years old who use social networking sites.
The Quinnipiac University Poll conducts nationwide surveys as a public service and for research. In one poll. participants were asked whether they thought eliminating the federal gas tax for the summer months is a good idea. The following problems are based on the results of that poll.
a. OfRepublicans, thought it a good idea, and, of Democrats, thought it a good idea. Obtain a confidence interval for the difference between the proportions of Republicans and Democrats who think that eliminating the federal gas tax for the summer months is a good idea.
b. Of women,thought it a good idea, and, of men, thought it a good idea. Obtain a confidence interval for the difference between the percentages of women and men who think that eliminating the federal gas tax for the summer months is a good idea.
Bank Breakup. In a nationwide survey, conducted by Pulse Opinion Research, LLC for Rasmussen Reports, a sample of American adults were asked whether they favor a plan to break up the megabanks, which currently control about of the banking industry; of those sampled responded in the affirmative. According to the report, "the margin of sampling error is percentage points with a level of confidence." Find and interpret a confidence interval for the percentage of all American adults who favor a plan to break up the megabanks.
1Neutropenia. Neutropenia is an abnormally low number o neutrophils (a type of white blood cell) in the blood. Chemotherapy often reduces the number of neutrophils to a level that makes the patient susceptible to fever and infections. G. Bucaneve et al. published a study of such cancer patients in the paper "Levofloxacin to Prevent Bacterial Infection in Patients With Cancer and Neutropenia" (New England Journal of Medicine, Vol. 353, No, 10, pp. 977-987). For the study. 375 patients were randomly assigned to receive a daily dose of levofloxacin, and 363 were given a placebo. In the group receiving levofloxacin, fever was present in 243 patients for the duration of neutropenia, whereas fever was experienced by 308 patients in the placebo group.
a. At the1% significance level, do the data provide sufficient evidence to conclude that levofloxacin is effective in reducing the occurrence of fever in such patients?
b. Find a98% confidence level for the difference in the proportions of such cancer patients who would experience fever for the duration of neutropenia
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