Heritage Union has said that 66% of U.S. adults have purchased life insurance. Suppose that for a random sample of 50 adults from a given U.S. city, research finds that only 56% of them have purchased life insurance. At a 0.05 level of significance test, is this sample finding significantly lower than the 66% reported by Heritage Union?
A scrap metal dealer claims that the mean of his cash sales is "no more than $80". But an IRS agent believes the dealer is untruthful. Observing a sample of 20 cash customers, the agent finds the mean purchase to be $91, with a standard deviation of $21.
A quality assurance inspector periodically examines the output of a machine to determine whether it is properly adjusted. When set properly, the machine produces nails with a mean length of 2.0 inches and a population standard deviation of 0.07 inches. For a sample of 35 nails, the mean length is 2.025 inches and the sample standard deviation is 0.065 inches.
The director of admissions at a large university says that 15% of high school juniors to whom she sends university pamphlets eventually apply for admission. In a sample of 300 students to whom materials were sent, 30 students applied for admission.
It is believed that the average number of years of experience of the employees at this location is 8.7 years. Examining a random sample of 15 employees, he finds the mean length to be 7.5 years with a standard deviation of 2.5 years. Does this sample indicate that the mean years of experience of employees is lower than 8.7?