Two high-school cross-country coaches fromdifferent teams are discussing their boys' andgirls' teams. One coach believes that male andfemale cross-country runners in the state ofIndiana differ in the number of miles they run,on average, each week. The other coachdisagrees. He feels that male and femalecross-country athletes run about the samenumber of miles per week, on average.Construct a 95% confidence interval for thedifference in average weekly mileage betweenmale and female cross-country runners in USAConsider the data obtained from twoindependent random samples:Boys: 20, 30, 35, 40, 40, 45, 45, 45, 50, 50, 50, 50, 52, 54, 55,60, 60, 60, 70, 75Girls: 20, 20, 30, 35, 35, 40, 40, 40, 45, 45, 45, 50, 50, 50, 52,60, 60, 60, 60, 60

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Answered: Two high-school cross-country coaches…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?

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What is meant by the sample space of an experiment?
The production manager in an automobile plant is concerned with the number of cars that do not pass the final quality control inspection. In the last two hours he noted that in a sample of 120 cars only 92 were acceptable. The lower and upper limit of a 95% confidence interval for the true percentage of all cars that would not pass the final quality control inspection would be:
A researcher surveys 50 individuals in Smithville and 40 in Amherst, finding that 30% of smithville residents moved last year, while only 22% of Amherst residents did. Is there enough evidence to conclude that mobility rates in the two communities differ? Use a two-tailored alternative, and a=0.10. Again, find the p-value and a 90% confidence interval for the difference in proportions
In order to judge the effectiveness of an advertising campaign for a certain brand of pretzel, a company obtained a simple random sample of 95 convenience store receipts the week before the ad campaign began, and found that 28 of them showed a purchase of the pretzels. Another simple random sample of 65 receipts was taken the week after the ad campaign, and 33 of them showed a pretzel purchase. Construct a 98% confidence interval for the difference between the proportions of customers purchasing pretzels before and after the ad campaign. Interpret the results. A marketing manager claims that the proportion of customers who purchased pretzels did not change after the ad campaign. Does the confidence interval contradict this claim?
A manager at ACME Equipment Sale and Rental wondered how offering a free two-year service warranty on its tractors might influence sales. For the next 500 customers expressing interest in purchasing a tractor, 250 were randomly offered the warranty and the rest were not. Ninety-three of those offered the warranty, and fifty-four of those not offered the warranty eventually purchased a tractor. a. Construct a 95% confidence interval for the difference between the proportions of customers purchasing tractors with and without warranties. Be sure to check all necessary assumptions, and interpret the interval. b. Test the hypothesis that offering the warranty increases the proportion of customers who eventually purchase a tractor. Be sure to check all necessary assumptions, state the null and alternative hypotheses, obtain the p-value, and state your conclusion. Should the manager offer the warranty based on this test?
A manager at ACME Equipment Sale and Rental wondered how offering a free two-year service warranty on its tractors might influence sales. For the next 500 customers expressing interest in purchasing a tractor, 250 were randomly offered the warranty and the rest were not. Ninety-three of those offered the warranty, and fifty-four of those not offered the warranty eventually purchased a tractor. a. Construct a 95% confidence interval for the difference between the proportions of customers purchasing tractors with and without warranties. Be sure to check all necessary assumptions, and interpret the interval.
In an October 2003 poll conducted by the Gallup organization, 684 of 1006 randomly selected adults aged 18 or older stated they think the government should make partial birth abortions illegal, except in cases necessary to save the mother. construct a 95 percent confidence interval for the proportion of adults 18 and older who think the government should make partial birth abortions illegal, except in cases necessary to save the mother and interpret the interval.
A tech company believes that the percentage of residents in the town XYZ that own a cell phone is 70%. A marketing manager believes the value to be different. He conducts a survey of 200 individuals and found that 130 responded yes to owning a cell phone. At a 95% confidence level, is there enough evidence to reject the null hypothesis.
It was found that in a sample of 90 teenage boys, 70% of them have received speeding tickets. What is the 90% confidence interval of the true proportion of teenage boys who have received speeding tickets?
In a two-sided confidence interval involving two groups, when the signs of its lower and upper boundaries are not the same, why does the difference between the means of the two groups is insignificant?
In a recent Zogby International Poll, nine of 48 respondents rated the likelihood of a terrorist attack in their community as “likely” or “very likely”. Use the “plus four” method to create a 98% confidence interval for the proportion of American adults who believe that a terrorist attack in their community is likely or very likely. Interpret your confidence interval.
The St. Lucie County Health Department needs to estimate the proportion of all children in the county aged 19-35 months that are completely up to date with all state-recommended immunizations. The St. Lucie County Health Department found that 67% of a random sample of children in the county aged 19-35 months were completely up to date with all state-recommended immunizations. Find three different confidence intervals - one with sample size 239, one with sample size 596, and one with sample size 937. Assume that 67% of the children each sample are completely up to date with all state recommended immunizations. Notice how the sample size affects the margin of error and the width of the interval. Report confidence interval solutions using interval notation. Report all solutions in percent form, rounded to two decimal places, if necessary. When n=239n=239, the margin of error for a 97% confidence interval is given b When n=239n=239, a 97% confidence interval is given by When n=596n=596,…

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