Question

A hospital administrator claims that the proportion of knee surgeries that are successful is 87%. To test this claim, a random sample of 450 patients who underwent knee surgery is taken and it is determined that 371 of these patients had a successful knee surgery operation. Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.

Answer 1

The test statistic for this hypothesis test for a proportion is -4.35.

Step-by-step explanation:

To test whether the proportion of successful knee surgeries claimed by the hospital administrator is accurate, we can conduct a hypothesis test for a proportion. The null hypothesis, denoted as H0, states that the true proportion of successful knee surgeries is equal to 87%. The alternative hypothesis, denoted as H1, states that the true proportion is not equal to 87%. We can use the formula for the test statistic for a proportion, which is calculated as (p - P) / sqrt((P(1-P))/n), where p is the sample proportion, P is the hypothesized proportion, and n is the sample size. Plugging in the values from the question, the test statistic is:

(371/450 - 0.87) / sqrt((0.87(1-0.87))/450) = -4.35