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- In the past decade, two presidential elections in the United States have witnessed very long wait times at precincts (voting stations) in states that ultimately decided the election (Florida in 2000 and Ohio in 2004). In Philadelphia as well, some voters complained about the long lines in some precincts, with most complaints coming from precinct A. In 2004, the average number of voters arriving at Precinct A was 35 per hour and the arrivals of voters was random with inter-arrival times that had a coefficient of variation of 1 (CVa=1). Philadelphia deployed 1 voting machine in Precinct A. Suppose that each voter spent on average 100 seconds in the voting booth (this is the time needed to cast her/his vote using a voting machine), with a standard deviation of 120 seconds. Given the long wait times for Precinct A, the city of Philadelphia is thinking of alternative solutions to improve voting conditions. One of the proposed solutions is as follows. Proposal 1: Deploy an additional voting…In the past decade, two presidential elections in the United States have witnessed very long wait times at precincts (voting stations) in states that ultimately decided the election (Florida in 2000 and Ohio in 2004).In Philadelphia as well, some voters complained about the long lines in some precincts, with most complaints coming from precinct A. In 2004, the average number of voters arriving at Precinct A was 35 per hour and the arrivals of voters was random with inter-arrival times that had a coefficient of variation of 1 (CVa=1).Philadelphia deployed 1 voting machine in Precinct A. Suppose that each voter spent on average 100 seconds in the voting booth (this is the time needed to cast her/his vote using a voting machine), with a standard deviation of 120 seconds.Q1. How long on average did a voter have to wait in line at precinct A in 2004 beforeentering a booth to cast her/his vote?A large nationwide survey showed that 65% of high school students like Coca-Cola better than Pepsi. Dr.Johnson conducted a small survey of randomly selected high school students in Michigan and found that 180 ofthe 300 surveyed students liked Coca-Cola better than Pepsi. Test if the proportion of students that preferCoca-Cola over Pepsi is significantly different than the percentage indicated by the nationwide survey with asignificance level of 5%.
- A nutritionist believes that obesity is more prevalent among American adults than it was in the past. He discovers that in a study conducted in the year 1994, 380 of the 1630 randomly chosen adults were classified as obese. However, in a more recent study, he finds 726 out of 2350 randomly chosen adults were classified as obese. At α = 0.05, do these studies provide evidence to support the nutritionist's claim that the proportion of obese adults has significantly increased since 1994?Each year, more than 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 have launched studies of drug-resistant gonorrhea.† Suppose that, of 205 cases tested in a certain state, 13 were found to be drug-resistant. Suppose also that, of 375 cases tested in another state, 7 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. (Let p1 = the population proportion of drug-resistant cases in the first state, and let p2 = the population proportion of drug resistant cases in the second state.) State the null and alternative hypotheses. (Enter != for ≠ as needed.) A. H0: Ha: B. a) Find the value of the test statistic. (Round your answer to two decimal places.) b) What is the p-value? (Round your answer to four decimal…It is believed that a sweetener called xylitol helps prevent ear infections. In a randomized experiment, 165 children took a placebo and 68 of them got ear infections. Another sample of 159 children took xylitol and 46 of them got ear infections. The scientists believe that the proportion of ear infections in the placebo group will be greater than the xylitol group. Test this hypothesis at α = 0.025.
- Each year, more than 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 have launched studies of drug-resistant gonorrhea.† Suppose that, of 221 cases tested in a certain state, 14 were found to be drug-resistant. Suppose also that, of 322 cases tested in another state, 6 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. (Let p1 = the population proportion of drug-resistant cases in the first state, and let p2 = the population proportion of drug resistant cases in the second state.) 1) State the null and alternative hypotheses. (Enter != for ≠ as needed.) 2) What is the test statistic & P-value? 3) what is the conclusion? A) Reject H0. There is a significant difference in drug resistance between the two states. B) Reject H0.…There have been many studies recently concerning coffee drinking and cholesterol level. While it is known that several coffee-bean components can elevate blood cholesterol level, it is thought that a new type of paper coffee filter may reduce the presence of some of these components in coffee. The effect of the new filter on cholesterol level will be studied over a 10-week period using 300 nonsmokers who each drink 4 cups of caffeinated coffee per day. Each of these 300 participants will be assigned to one of two groups: the experimental group, who will only drink coffee that has been made with the new filter, or the control group, who will only drink coffee that has been made with the standard filter. Each participant’s cholesterol level will be measured at the beginning and at the end of the study. Describe an appropriate method for assigning the subjects to the two groups so that each group will have an equal number of subjects. In this study, the researchers chose to include a…There have been many studies recently concerning coffee drinking and cholesterol level. While it is known that several coffee-bean components can elevate blood cholesterol level, it is thought that a new type of paper coffee filter may reduce the presence of some of these components in coffee. The effect of the new filter on cholesterol level will be studied over a 10-week period using 300 nonsmokers who each drink 4 cups of caffeinated coffee per day. Each of these 300 participants will be assigned to one of two groups: the experimental group, who will only drink coffee that has been made with the new filter, or the control group, who will only drink coffee that has been made with the standard filter. Each participant’s cholesterol level will be measured at the beginning and at the end of the study. Which test would you conduct to determine whether the change in cholesterol level would be greater if people used the new filter rather than using the standard filter? Why would the…
- A researcher is comparing the occurrence of nausea as a side-effect in two brands of medication: Brand A and Brand B. For a random sample of 150 Brand A users, 66 experienced nausea as a side-effect. For a random sample of 200 Brand B users, 118 experienced nausea as a side-effect. Can the researcher conclude that the proportion of all Brand A users who experience nausea as a side-effect is different from the proportion of all Brand B users who experience nausea as a side-effect. For the hypothesis testing scenario above, the researcher concludes that the two proportions are different at the 0.01 significance level. Compute the 99% confidence interval to estimate the difference.A doctor is concerned about the relationship between blood pressure and irregular heartbeats.Among her patients, she classifies blood pressures as high, normal, or low and heartbeats asregular or irregular and finds that:• 16% have high blood pressure;• 19% have low blood pressure; • 17% have an irregular heartbeat;• of those with an irregular heartbeat, 35% have high blood pressure; and• of those with normal blood pressure, 11% have an irregular heartbeat.What percentage of her patients have a regular heartbeat and low blood pressure?A young professor found out from a senior professor that psychology students in St. Alex University tend to do good in their Social Science subject, claiming that historically, the mean grade of psych students in the said course is 1.50. Curious if this claim was true, the young professor took a random sample of 9 students who took Social Science subject. Before collecting data, he was undecided about his own claim because he knew of some students who did really good in the course but has also encountered others who did poorly. He found that their mean grade for the course is 1.35 with a standard deviation of 0.50. Use the Test of Significance Approach in testing the young professor’s claim. a. Estimate μ at 90% confidence interval. b. Between z and t, which is more appropriate to use given the data? Why? c. What are the chances that your estimate of μ was wrong? Describe and explain a potential source of error to your estimate. d. Holding % of CI constant, what can you do to lower…
