The mayor of a town has decided to support the development of a new highway by their town. The vote for the measure is scheduled for a month from now and the mayor is concerned that they may not have the majority of votes to pass this motion. They commission a survey that asks likely voters if they plan to vote for the measure. Of the 4175 people selected at random from likely voters, 3128 said they would vote in support of the new highway. Find the lower limit of the 95% confidence interval for the true proportion of voters who will vote for the measure.
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Only round final answer to 3 decimal places.
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- 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…In a sample of 40 mice, a biologist found that 42% were able to run a maze in 30 seconds or less. Find the 90% limit for the population proportion of mice who can run a maze in 30 seconds or less.The manager of a theater that is open to residents of two towns, A and B, wants to know if the proportion of households from A that use the library is smaller than the proportion of households from B. In order to test this, the manager asks 45 households in A and 49 households in B whether anyone in their household had used the theater last summer. 23 of the households surveyed in A responded "yes", and 35 of the households in B responded "yes". Find the p-value that would be used to make a conclusion for this hypothesis test.
- The rabies vaccine for dogs can save your dog's life. If your dog bites another animal or is on the receiving end of a bite, the vaccine can protect them from a dangerous and potentially fatal illness. Furthermore, in most places, the rabies vaccine for dogs is legally required. The NYC Department of Health wants to know if LESS than 95% of the dogs in the city have been vaccinated with their rabies vaccine. 158,045 of the 165,000 dogs examined had their rabies shots. Risk no more than 5% Type I error. Do you retain or reject the null hypothesis? Retain the null. Reject the null.The rabies vaccine for dogs can save your dog's life. If your dog bites another animal or is on the receiving end of a bite, the vaccine can protect them from a dangerous and potentially fatal illness. Furthermore, in most places, the rabies vaccine for dogs is legally required. The NYC Department of Health wants to know if LESS than 95% of the dogs in the city have been vaccinated with their rabies vaccine. 158,045 of the 165,000 dogs examined had their rabies shots. Risk no more than 5% Type I error. What is the probability of Z OBT being more than alphs? (round to the nearest hundredth)The rabies vaccine for dogs can save your dog's life. If your dog bites another animal or is on the receiving end of a bite, the vaccine can protect them from a dangerous and potentially fatal illness. Furthermore, in most places, the rabies vaccine for dogs is legally required. The NYC Department of Health wants to know if LESS than 95% of the dogs in the city have been vaccinated with their rabies vaccine. 158,045 of the 165,000 dogs examined had their rabies shots. Risk no more than 5% Type I error. What is the zcrit?