(a) Dr. Mehta, a noted social psychologist, surveyed 180 top executives and found that 45 percent of them were unable to add fractions correctly. Construct a 98 percent confidence interval for the true proportion of top executives who cannot correctly add fractions.
2. A traffic control officer reports that 70% of the trucks passing through a checkpoint are from outside the Dhaka city. What is the probability that at least four of the next six trucks are from outside the city?
3. The incidence of occupational disease in an industry is such that the workers have a 23% chance of suffering from it. What is the probability that out of 9 workers, 7 or more will contract the disease?
4. The USDA limit for a certain type of contamination for chicken is 25%. A meat packing company claims that its chicken falls within the limit. You perform a hypothesis test to determine whether the company's claim is true. When will a type I error and type II error occur? Which one is more serious? Why?