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Suppose a sample of 600 surgeries with the new scrubs shows 18 infections. Find the value of the test statistic, z, and explain its meaning in context. The old infection rate was 4%.

User Pankhuri
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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.

User Stony
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