Question

Below are some examples of hypothesis testing questions. Match the correct test to the question.

- 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, a 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 purchased 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 population standard deviation of 0.07 inches. For a sample of 35 nails, the mean length is 2.025 inches and sample standard deviation of 0.065 inches.

- The director of admissions at a large unviersity 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 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?

A. sample proportions, z-test, two-sided (tail)

B. sample means, t-test, one-sided (tail)

C. sample means, z-test, one-sided (tail)

D. sample means, z-test, two-sided (tail)

E. sample means, t-test, two-sided (tail)

F. sample means, t-test, one sided (tail)

G. sample proportions, z-test, one-sided (tail)

Answer 1

Example 1: sample proportions, z-test, one-sided (tail) (upper tail), since here we are checking whether the population proportion is lower than 0.66.

Example 2: sample means, t-test, one-sided (tail) (upper tail), since here we are checking whether the population mean is greater than $80 or not.

Example 3: sample means, z-test, two-sided (tail), since here are checking whether the population mean is 2.0 inches or not and the population s.d. is also given.

Example 4: sample proportions, z-test, two-sided (tail), since here we are checking whether the population proportion is equal to 0.15 or not.

Example 5: sample means, t-test, one sided (tail) (lower tail), since here we are checking whether the population mean is lesser than 8.7 or not.