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.

(a) Should we use a one-sided or a two-sided test? Explain your reasoning.

(b) Should we use a paired or non-paired test? Explain your reasoning.

(c) Should we use a t-test or a z-test? Explain your reasoning.

Answer 1

Result:

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.

(a) Should we use a one-sided or a two-sided test? Explain your reasoning.

We should use two tailed test. We like to compare the two years average. We are interested to see whether the test parameter calculated for the two years are different. ( There is no specific comparison of one year is greater or lesser than the other year).

(b) Should we use a paired or non-paired test? Explain your reasoning.

We should us Paired t test, because same samples are observed in   two years. The observations are paired.

(c) Should we use a t-test or a z-test? Explain your reasoning.

We should use t test because population standard deviation is not known and sample size is less than 30.