7. (简答题 6.0分) Suppose that 75% of people in a certain metropolitan area live in the city and 25% of the people live in the suburbs. If 1200 people attending a certain concert represent a random sample from the metropolitan area, what is the probabilty that the number of people from the suburbs attending the conert will be fewer than 270?($(2)=0.9772 (1)=0.8413 (3)=0.9987 (333) = 0.9996
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- Suppose that the average height of men in the United States is approximately normallydistributed with a mean of approximately 70 inches and a standard deviation ofapproximately 4 inches. (a) If you take a sample of 4 men, find Pr {68 ≤ Y̅ ≤ 73}, the probability that the sample mean Y̅ will be between 68 and 73 inches. (b) If you take a sample of 16 men, find Pr {68 ≤ Y̅ ≤ 73}, the probability that the sample mean Y̅ will be between 68 and 73 inches. (c) If you take a sample of n men where n > 16, which one of the following is true? (circle one of the three statements.)Pr{68 ≤ Y̅ ≤ 73} > the probability that you found in (b)Pr{68 ≤ Y̅ ≤ 73} = the probability that you found in (b)Pr{68 ≤ Y̅ ≤ 73} < the probability that you found in (b)A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 35 adult Americar sample proportion of adults who respond yes, is approximately normal, how many more adult Amencans does the.researcher ne (a) 10% of all adult Americans support the changes (b) 15% of all adult Americans support the changes (a) The researcher must ask more American adults. (Round up to the nearest integer) (b) The researcher must ask more American adults (Round up to the nearest integer.)7. Suppose a researcher wants to estimate the difference in proportions of firstborn between the college graduates and non-graduates to within 0.05, with 90% confidence. How many college graduates and non-graduates must he interview, assuming that an equal number will be interviewed from each group?
- A simple random sample of 10 pages from a dictionary is obtained. The numbers of words defined on those pages are found, with the results n = 10, x- 63.6 words, s= 15.8 words. Given that this dictionary has 1465 pages with defined words, the publisher's claim that there are more than 70,000 defined words is equivalent to the claim that the mean number of words per page is greater than 47.8 words. Use a 0.10 significance level to test the claim that the mean number of words per page is greater than 47.8 words. Identify the null and alternative hypotheses, P- value, and state the final conclusion that addresses the original claim. Assume that the population is normally distributed. What are the null and alternative hypotheses? O A. Ho: µ= 47.8 words O B. Ho:µ=47.8 words H:µ 47.8 words O D. Ho: H= 47.8 words H,:µ> 47.8 words H1:µ< 47.8 words Determine the P-value. (Round to three decimal places as needed.)How many different simple random samples of size 5 can be obtained from a population whose size is 38? The number of simple random samples which can be obtained is ???25. An experimenter has prepared a drug that he claims has side effects in 25% or less of those people taking it (considerably less than the current medication). In an attempt to verify the claim, his prescribed drug was administered to 24 patients & Y, the # of patients having side effects by the drug, was observed. If at most 9 patients have side effects with this drug the claim is accepted (as valid). Find P (Type II Error) when p = 0.75 0.000112 0.000523 O 0.595599 None of the other answers are correct. O 0.999888 O 0.999477
- Not all visitors to a certain company's website are customers or potential customers. In fact, the company's executives estimate that about 10% of all visitors to the website are looking for other websites. Assume that this estimate is correct and that a random sample of 40 visitors to the website is taken. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of visitors in the sample who actually are looking for the company's website by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.Suppose that a recent article by a historian stated that the mean time spent in jail by a first–timeconvicted burglar in the 20th century was 2.5 years. A study was then done to see if the mean time has increasedin the new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The meanlength of time in jail from the survey was 3 years. Suppose that it is somehow known that the population standarddeviation is 1.8 years and that the population is normally distributed.The hypotheses can then be framed as:H0 : μ = 2.5 vs. Ha : μ > 2.5(a) Which of the following figures (next page) best describes the p-value for this hypothesis testingproblem. Explain your reasoning. (numbers above red shaded area represent the corresponding probabilities). (b) Write the decision and conclusion for this hypothesis testing problem if the significance level, α,is 0.1.Can i get help with this problem? the sample proportion denoted phat is given by the formula phat(p-hat)=x/n where x s the number of individuals with a specified characteristic in a sample of n individuals. 1. find: phat(p-hat_ if the students poll surveyed 1200 people that vacation during the summer and asked if they plan to work while on vacation. Of those surveyed, 552 indicated that they plan to work on vacation. Find the sample proportion of individuals polled that plan to work on vacation. So, Students estimates that from the value of phat(p-hat) found above that ____________ or ________ % of adults who vacation plan to work on vacation,
- 39 - In a study on life satisfaction in urban and rural areas of a province, 453 people in the urban area and 345 people in the rural area were randomly selected and the subjects were asked whether they were satisfied with their lives. 92 people in urban areas and 56 people in rural areas stated that they were not satisfied with their lives. Which of the following is the point estimate of the difference in the ratios of those who are satisfied with their lives in the urban and rural areas of this province? a) 0.02 B) 0.18 NS) -0.04 D) -0.18 TO) 0.04Not all visitors to a certain company's website are customers or potential customers. In fact, the company's executives estimate that about 12% of all visitors to the website are looking for other websites. Assume that this estimate is correct and that a random sample of 40 visitors to the website is taken. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of visitors in the sample who actually are looking for the company's website by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.
