Question

Nineteen people move out of a neighborhood; four are minorities. Of the nineteen, eight move onto a block with new housing, and one of these eight is a minority. How likely is it that, if there were no discrimination, less than two people out of the eight people on this new block would be minorities? If the resulting probability is less than 0.05, evidence for discrimination exists. Does such evidence exist in this case?

Answer 1

Proportion of minorities, p = 4/19 = 0.2105263

If there were no discrimination, Standard error of proportion (using finite population correction) is,

Sample proportion, = 1/8 = 0.125

Test statistic, z = ( - p) / SE = (0.125 - 0.2105263) / 0.1126775

= -0.76

Probability that less than two people out of the eight people on this new block would be minorities

= P(z < -0.76)

= 0.2236

Since the resulting probability is not less than 0.05, there is no significant evidence for discrimination exists.