According to the Census, a certain town has a population of 20000 people age 18 and over. Of them, 10% have incomes over $75000 a year. i) As part of a pre-election survey, a simple random sample of 100 people will be drawn from this population. What is the chance that exactly 10 people in the sample have incomes over $75000 a year? ii) A simple random sample of 100 people will be drawn from this population. Find the chance that 12% or more of the people in the sample have incomes over $75000 a year. iii) If a SRS of 10000 people are drawn from the population instead, how far off should you expect the survey organization to be in estimating the percentage of people that have income over $75000 a year? - The National Assessment of Educational Progress administers standardized achievement test to nationwide samples of 17 year-olds in school. One year, the tests covered history and literature. You may assume that a simple random sample of size 6000 was taken. Only 2166 of students in the sample knew that Chaucer wrote the Canterbury Tales. i) The range from ____ to _____ is a 95%-confidence interval for the percentage of students who knew that Chaucer wrote the Canterbury Tales among_______________________ Fill in the first two blanks with numbers. And fill in the last blank with one of the two options: \"all the 17 year olds in the population\" or \"6000 people in the sample\" ii) Fill in the blank with a number and explain: \"A 95 % confidence interval based on a sample of _________ people will be about half as wide as the one based on a sample of 6000 people\" - One year, there were about 600,000 faculty members at institutions of higher learning in the U.S. As part of its study, the Carnegie Commission took a simple random sample of 2,500 of these faculty persons, and worked out the 95% confidence interval for the average number of research papers published by all 600,000 faculty members in the two years prior to the survey. The 95% confidence interval was 1.62 to 1.78 papers. i) Fill in the blanks with numbers: on the average, the 2,500 sample persons had published _____ papers and the SD was ________ papers. ii) True or False, and explain why: \" There is a 95 % chance that the population average is between 1.62 and 1.78.\" iii) True or False, and explain why: \"About 95% of the people in the population published between 1.62 and 1.78.\