Assignment 1-? 3 Name: 1) Your manager has collected some data regarding spare time of workers in minutes from a sample of 23 workers. The average spare time is 58 minutes with the sample standard deviation of 7 minutes. Construct the 98% confidence interval of spare time in the factory. (4 marks) 2) 380 students were surveyed for their course selection options for the next semester. 180 of the students stated that they will choose statistics. a) Construct the 95% condence interval for the true proportion of this school's students who will choose statistics next semester. (4 marks) b) How many students should be surveyed if the desired margin of error is to be 0.04? (4 marks) 3) A sample of 48 students were asked about how much time they spend studying before the midterm exam. The average is 8 hours with the standard deviation of 25 min. Construct and interpret the 90% confidence interval about the average time all students study before the midterm exam? (4 marks) 4) Early study results show that 78% of customers are willing to pay an extra dollar on their purchase to a local charity. If the margin of error is 0.012 at 95% confidence, find how many customers are surveyed. (4 marks)