Question

Set up hypotheses for the following situations and explain your reasoning (One-tail or two-tailed? What are your null and alternate hypotheses? Why?). Indicate whether a z-test or t-test would be recommended to evaluate the hypotheses. If a t-test is recommended, how many degrees of freedom should be used?

1. The EU wants to examine statistics on refugees’ ages. Historically, the mean age of refugees arriving in Europe is 27.5 years old with a standard deviation of 3.1 years. In 2015, the EU conducted a simple random sample of 250 recently arriving refugees and wants to determine whether their age has declined compared to the historical average.

2. A monitoring station set up near the Panama Canal records daily passage of vessels. A researcher obtains the daily records for the most recent year to compare with the daily data from a period of five years ago, which shows a historical mean of 140 vessels per day and a standard deviation of 12. The older data can be treated as the population for purposes of this test. The researcher is investigating international trade and wants to determine whether the mean of daily passage has changed in the most recent one-year period.

3. A International Relations student team is evaluating the effectiveness of a new OECD development assistance program in improving women’s socioeconomic welfare in developing countries. Current data shows that women in developing countries earn on average $2.97 per day, and this daily income is believed to be normally distributed, but the population standard deviation is not known. The new program will be adopted only if it significantly increases women’s daily income. Because of the limited funding for the team, it is expected that the sample will consist of only 23 women.

Answer 1

1. The hypothesis being tested is:

H₀: µ = 27.5

H_a: µ < 27.5

This is a one-tailed test.

This is a z-test because the population standard deviation is known.

2. The hypothesis being tested is:

H₀: µ = 140

H_a: µ ≠ 140

This is a two-tailed test.

This is a z-test because the population standard deviation is known.

3. The hypothesis being tested is:

H₀: µ = 2.97

H_a: µ > 2.97

This is a one-tailed test.

This is a t-test because the population standard deviation is unknown.