Question

Medical Operations

The director of a medical hospital feels that her surgeons perform fewer operations per year than the national average of 211. She selected a random sample of 15 surgeons and found that the mean number of operations they performed was 208.8. The standard deviation of the sample was 3.8. Is there enough evidence to support the director’s feelings at α = 0.10?

Answer 1

To determine if there is enough evidence to support the director's feelings that the surgeons perform fewer operations per year than the national average, we conduct a hypothesis test.

Step-by-step explanation:

To determine if there is enough evidence to support the director's feelings that the surgeons perform fewer operations per year than the national average, we need to conduct a hypothesis test. The null hypothesis, H0, states that the mean number of operations performed by the surgeons is equal to the national average (μ = 211).

The alternative hypothesis, Ha, states that the mean number of operations performed by the surgeons is less than the national average (μ < 211).

In this case, we will use a one-sample t-test since the population standard deviation is unknown. With a sample size of 15 and a sample mean of 208.8, we can calculate the test statistic using the formula:

t = (sample mean - population mean) / (sample standard deviation / √sample size)

Using the given values, t = (208.8 - 211) / (3.8 / √15) = -0.4

We can compare this test statistic to the critical t-value at α = 0.10 with degrees of freedom equal to the sample size minus 1. In this case, the critical t-value is approximately -1.345. Since the test statistic (-0.4) is greater than the critical t-value (-1.345), we fail to reject the null hypothesis.

Therefore, there is not enough evidence to support the director's feelings that the surgeons perform fewer operations per year than the national average.