ESS210B
Prof. Jin-Yi Yu
Example
qThere is a data set that contains the percentage of women in the work force in 1968 and 1972 from a sample of 19 cities. There are two observations from each city, and the observations constitute paired data. You are asked to determine whether this sample demonstrates a statistically significant increase in the percentage of women in the work force.
qAnswer:
q    1. Ho: m = 0 (There is no change in the percentage)
q        H1: m¹ 0 (There is some change, but we are not assuming the
q                        direction of change)
q    2. 95% t-Test with N=19 è We can determine t0.25% and t0.975%
q    3. S=0.05974 è s = S/(19)0.5 = 0.01371
q    4. t statistic t = (0.0337 – 0) / s = 2.458 > t0.975%
q      5. We reject the null hypothesis è There has been a significant change
q         in women’s participation in the work force in those 4 years.
q
mean increase in the
Percentage from 19 cities