In recent poling, it has been suggested that the approval rating of a certainpolitician (the proportion of people polled that approve of his performance in office)is 40%.1)Suppose we conduct a new poll consisting of 30 people.Assuming thesuggested approval rating is correct, and the independence of people polled,if X was the number of people in this new poll who approve of the politician,what kind of distribution would x have and what are its parameters?2)Assuming the facts in the previous problem, how many people would we expectto see in the new poll who approve of the candidate? Suppose the approvalrating in the new poll is 30%. How many people would approve of thecandidate in this case?3) Again, given the facts in problem 1, what is the probability of seeing ahigher approval rating in the new poll (more than expected in problem 2)?4)After taking the new poll, we find that 9 out of the 30 people polled approveof the politician's performance in office. Calculate a 95% confidenceinterval for the true approval rating (or rather, the population proportionof people who approve of the politician's performance).5) If we want the margin of error in the previous interval to be less than 2%,how many people should we poll in total?6) Does 40% fall into the confidence interval in problem 4? Does this suggestthat the politician's approval rating has fallen significantly, or do we neemore data?

Given that: The proportion of people polled that approve of his performance in office is 40% That…

Answered: In recent poling, it has been suggested…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A fitness course claims that it can improve an individual's physical ability. To test the effect of a physical fitness course on one's physical ability, the number of sit-ups that a person could do in one minute, both before and after the course, was recorded. Ten individuals are randomly selected to participate in the course. The results are displayed in the following table. Can it be concluded, from the data, that participation in the physical fitness course resulted in significant improvement? Let d=(number of sit-ups that can be done after taking the course)−(number of sit-ups that can be done prior to taking the course)d=(number of sit-ups that can be done after taking the course)−(number of sit-ups that can be done prior to taking the course). Use a significance level of α=0.05α=0.05 for the test. Assume that the numbers of sit-ups are normally distributed for the population both before and after taking the fitness course. Sit-ups before 3232 4545 2121 5050 3636 4444 2626 2020…
In a survey of 1000 adult Americans, 45.7% indicated that they were somewhat interested or very interested in having web access in their cars. Suppose that the marketing manager of a car manufacturer claims that the 45.7% is based only on a sample and that 45.7% is close to half, so there is no reason to believe that the proportion of all adult Americans who want car web access is less than 0.50. Is the marketing manager correct in his claim? Provide statistical evidence to support your answer. For purposes of this exercise, assume that the sample can be considered as representative of adult Americans. Test the relevant hypotheses using ? = 0.05. Find the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z= P-value= chose the conclusion in the context of the problem. a) Reject H0. We do not have convincing evidence that the proportion of all adult Americans who want car web access is less than 0.5. The marketing…
The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains (Consumer Reports website). One of the variables in the study is meal price, the average amount paid per person for dinner and drinks, minus the tip. Suppose a reporter for the Sun Coast Times thought that it would be of interest to her readers to conduct a similar study for restaurants located on the Grand Strand section in Myrtle Beach, South Carolina. The reporter selected a sample of 8 seafood restaurants, 8 Italian restaurants, and 8 steakhouses. The following data show the meal prices ($) obtained for the 24 restaurants sampled. Use a = 0.05 to test whether there is a significant difference among the mean meal price for the three types of restaurants. Source Sum of Squares Degrees Mean Square F P-value of Variation (to whole number) of Freedom (to 2 decimals) (to 2 decimals) (to 4 decimals) X X (X) * X * * Treatments Error Total The p-value is less than 0.01…
A fitness course claims that it can improve an individual's physical ability. To test the effect of a physical fitness course on one's physical ability, the number of sit-ups that a person could do in one minute, both before and after the course, was recorded. Ten individuals are randomly selected to participate in the course. The results are displayed in the following table. Can it be concluded, from the data, that participation in the physical fitness course resulted in significant improvement? Let d=(number of sit-ups that can be done after taking the course)−(number of sit-ups that can be done prior to taking the course)d=(number of sit-ups that can be done after taking the course)−(number of sit-ups that can be done prior to taking the course). Use a significance level of α=0.05 for the test. Assume that the numbers of sit-ups are normally distributed for the population both before and after taking the fitness course. Sit-ups before 42 42 23 32 30 42 25 47 35 38 Sit-ups after…
A fitness course claims that it can improve an individual's physical ability. To test the effect of a physical fitness course on one's physical ability, the number of sit-ups that a person could do in one minute, both before and after the course, was recorded. Ten individuals are randomly selected to participate in the course. The results are displayed in the following table. Can it be concluded, from the data, that participation in the physical fitness course resulted in significant improvement? Let d=(number of sit-ups that can be done after taking the course)−(number of sit-ups that can be done prior to taking the course)d=(number of sit-ups that can be done after taking the course)−(number of sit-ups that can be done prior to taking the course). Use a significance level of α=0.05 for the test. Assume that the numbers of sit-ups are normally distributed for the population both before and after taking the fitness course. Sit-ups before 42 42 23 32 30 42 25 47 35 38 Sit-ups after…
Suppose that 75% of adults agree that, while downloading music from the Internet and then selling it is piracy and should be prohibited, downloading for personal use is an innocent act and should not be prohibited. We'll take a random sample of 30 adults and ask if they agree with the statement. Then the sampling distribution of the sample proportion of people who answer yes to the question is:
Among college students, the proportion p who say they’re interested in their congressional district’s election results has traditionally been 75% . After a series of debates on campuses, a political scientist claims that the proportion of college students who say they’re interested in their district’s election results is more than 75% . A poll is commissioned, and 207 out of a random sample of 275 college students say they’re interested in their district’s election results. Is there enough evidence to support the political scientist's claim at the 0.01 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H0 and the alternative hypothesis H1 . H0: H1: (b) Determine the type of test statistic to use. ▼(Choose one) (c) Find the value of the test statistic. (Round…
"Bluth's Original Frozen Banana Stand" is a frozen banana stand founded in 1953 by George Bluth. They offer multiple types of chocolate that you can have your frozen banana dipped in, and they also offer multiple different toppings for your frozen banana. One day when stand employee Michael was working, he wondered whether or not there was a relationship between what customers had their bananas dipped in (milk chocolate, white chocolate, or dark chocolate) and their choice of topping (plain, walnuts, or sprinkles). He recorded the choices of each for 90 different customers, and the resulting data can be seen in the table below. Which cell has the highest Chi Square contribution? Chocolate milk milk milk white white white dark dark dark walnuts, milk Osprinkles, white walnuts, dark O plain, dark Topping plain walnuts sprinkles plain walnuts sprinkles plain walnuts sprinkles Freq. 15 4 11 7 13 10 14 10
A fitness course claims that it can improve an individual's physical ability. To test the effect of a physical fitness course on one's physical ability, the number of sit-ups that a person could do in one minute, both before and after the course, was recorded. Ten individuals are randomly selected to participate in the course. The results are displayed in the following table. Can it be concluded, from the data, that participation in the physical fitness course resulted in significant improvement? Let d=(number of sit-ups that can be done after taking the course)−(number of sit-ups that can be done prior to taking the course)d=(number of sit-ups that can be done after taking the course)−(number of sit-ups that can be done prior to taking the course). Use a significance level of α=0.05α=0.05 for the test. Assume that the numbers of sit-ups are normally distributed for the population both before and after taking the fitness course. Sit-ups before 3030 3939 5353 3838 3333 5151 2222 3838…
b) A certain pay television company wishes to estimate the proportion of its customers who would purchase a pay television program guide. To do this, the company manager decides to select a random sample of customers and note the number who would purchase a program guide. Suppose that experience in other areas suggests that about 13% of customers will purchase a program guide. How many customers should the company manager include in his sample if he wishes to estimate the true proportion who will purchase the program guide correct to within 5% (0.05) with a confidence level of 95%?
Students at Hereford High School want to investigate whether they have more school spirit than students at Blake High School. To test this hypothesis, the students will select a random sample of students from each school and determine the proportion of the sampled students who wear school colors to their respective pep rallies. Let pHpH represent the proportion of Hereford students who wear school colors to their pep rally and pBpB represent the proportion of Blake students who wear school colors to their pep rally. Which of the following are the correct null and alternative hypotheses for the investigation? H0:pH−pB=0Ha:pH−pB≠0H0:pH−pB=0Ha:pH−pB≠0 A H0:pH−pB=0Ha:pH−pB>0H0:pH−pB=0Ha:pH−pB>0 B H0:pH−pB=0Ha:pH−pB<0H0:pH−pB=0Ha:pH−pB<0 C H0:pH−pB>0Ha:pH−pB=0H0:pH−pB>0Ha:pH−pB=0 D H0:pH−pB<0Ha:pH−pB=0
A sample of 274 adults is selected. The adults are classified according to voter registration status ("registered" or "not registered"). They are also classified according to preferred source of current events information ("television", "newspapers", "radio", or "internet sites"). The results are given in the contingency table below. Registered X Not registered Television 30 35 Newspapers Radio 42 37 What is the relative frequency of adults in the sample who are not registered to vote? Round your answer to two decimal places. 0 37 33 Internet sites 16 44

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