Answer to Question #120474 in Statistics and Probability for Joseph Se

Question

Air quality measurements were collected in a random sample of 25 country capitals in 2013, and then again in the same cities in 2014. We would like to use these data to compare average air quality between the two years. Which of the following tests is the most appropriate?

A. paired t-test with one-sided alternative hypothesis
B. independent samples t-test with two-sided alternative hypothesis
C. paired t-test with two-sided alternative hypothesis
D. independent samples t-test with one-sided alternative hypothesis

2. We are testing the following hypotheses:

H0: μ1 = μ2
HA: μ1 is not equal to μ2

The sample sizes are n1 = 20 and n2 = 40. Your friend who is working on this hypothesis test calculates a Z statistic, Z = 2.5. Which of the following is true?

A. She should be using an F statistic instead of a Z statistic.
B. p-value is approximately 0.006.
C. She should be using a T statistic instead of a Z statistic.
D. p-value is approximately 0.012.

Answer 1

1) C. paired t-test with two-sided alternative hypothesis

Two-sided, we are evaluating a difference, not in a particular direction. Paired, data are recorded in the same cities at two different time points. The temperature in a city at one point is not independent of the temperature in the same city at another time point. t-test, sample is small and population standard deviation is unknown.

2) C. She should be using a T statistic instead of a Z statistic.

sample is small and population standard deviation is unknown.