To find the test statistic, we need to use the formula:
z = (p - P) / sqrt[(P * (1 - P)) / n]
where:
p = sample proportion = 15/20 = 0.75
P = hypothesized population proportion = 0.42
n = sample size = 20
Plugging in the values, we get:
z = (0.75 - 0.42) / sqrt[(0.42 * 0.58) / 20]
z = 2.11
Therefore, the test statistic is 2.11.