Question

The director of a medical hospital feels that her surgeons perform more operations per year than the national average of X. She selected a random sample of surgeons and found that the mean number of operations they performed was Y. The standard deviation of the sample was Z. Is there enough evidence to support the director's feelings at a significance level of α? Assume that the population is approximately normally distributed. Use the critical value method and tables.

a. Yes, there is enough evidence.
b. No, there is not enough evidence.

Answer 1

To determine if there is enough evidence to support the director's feelings, conduct a hypothesis test using the critical value method.

Step-by-step explanation:

To determine whether there is enough evidence to support the director's feelings that her surgeons perform more operations per year than the national average, we can conduct a hypothesis test using the critical value method:

1. Null Hypothesis: The mean number of operations performed by the surgeons is equal to the national average (X).
2. Alternative Hypothesis: The mean number of operations performed by the surgeons is greater than the national average (X).
3. Calculate the test statistic: Z = (Y - X) / (Z / sqrt(n)), where Y is the sample mean, X is the national average, Z is the sample standard deviation, and n is the sample size.
4. Find the critical value corresponding to the significance level (α).
5. Compare the test statistic to the critical value. If the test statistic is greater than the critical value, reject the null hypothesis, indicating there is enough evidence to support the director's feelings.
6. Conclusion: If the null hypothesis is rejected, the answer is 'a. Yes, there is enough evidence.' If the null hypothesis is not rejected, the answer is 'b. No, there is not enough evidence.'