Final answer:
To determine if new surgical scrubs have changed the infection rate, a z-test statistic of -1.96 is calculated using the sample proportion of infections. This statistic shows how many standard deviations the sample proportion is from the hypothesized infection rate.
Step-by-step explanation:
The question involves a statistical hypothesis test comparing two proportions to determine if the new scrubs have led to a change in the infection rate from the old rate of 4%. To find the test statistic, z, we use the formula:
z = (p - P0) / (√(P0(1 - P0) / n))
Where p is the sample proportion, P0 is the null hypothesis proportion (0.04 in this case), and n is the sample size.
In this scenario, p = 18/600 = 0.03. Inserting the values, we get:
z = (0.03 - 0.04) / √(0.04(1 - 0.04) / 600) = -1.96
The z-test statistic of -1.96 indicates the number of standard deviations the sample proportion of 3% is below the hypothesized population proportion of 4%. This result is used to determine the p-value for the hypothesis test, which then can compare to a significance level to decide whether to reject or not reject the null hypothesis.