Question

A hospital director believes that more than 61% of the test tubes contain errors and feels an audit is required. A sample of 210 tubes found 147 errors. Is there sufficient evidence at the 0.05 level to substantiate the hospital director's claim?

State the null and alternative hypotheses for the above scenario.

Answer 1

Step-by-step explanation:

To determine if there is sufficient evidence to support the hospital director's claim, you can perform a hypothesis test. The null hypothesis is that the proportion of test tubes with errors is less than or equal to 0.61 (61%), and the alternative hypothesis is that the proportion of test tubes with errors is greater than 0.61 (61%).

Using the sample of 210 tubes, you can calculate the sample proportion of tubes with errors, which is 147/210 = 0.7. You can also calculate the standard error of the proportion, which is the standard deviation of the sampling distribution of the proportion.

Then, you can use a z-test to calculate the test statistic and p-value. The test statistic is (0.7-0.61) / (standard error of proportion).

If the p-value is less than 0.05, then you can reject the null hypothesis and conclude that there is sufficient evidence to support the hospital director's claim that more than 61% of the test tubes contain errors.

You can use the sample data and a calculator or a software to calculate the p-value and the test statistic. It is also important to consult with a statistician.