Question

Hypothesis Tests and Confidence Intervals for Hemoglobin

a. Exercise 2 includes a confidence interval. If you use the P-value method or the critical value method from Part 1 of this section to test the claim that women and men have the same mean hemoglobin levels, will the hypothesis tests and the confidence interval result in the same conclusion?

b. In general, if you conduct a hypothesis test using the methods of Part 1 of this section, will the P-value method, the critical value method, and the confidence interval method result in the same conclusion?

c. Assume that you want to use a 0.01 significance level to test the claim that the mean haemoglobin level in women is lessthan the mean hemoglobin level in men. What confidence level should be used if you want to test that claim using a confidence interval?

Short answer

a. Yes, the hypothesis tests and the confidence interval results in the same conclusion.

b. Yes. The -value method, the critical value method, and the confidence interval method result in the same conclusion.

c. Confidence level should be used.

Step-by-step solution

Define inferential tests

a. Refer to exercise 2 for the claim that mean haemoglobin level in men and women is same.

The test is two-tailed.

The p-value method or critical value method pertaining to the claim would provide the same results for the test at the same level of significance. Further, the results derived from any of the two methods of hypothesis tests would be the same as the result derived from the confidence level at any corresponding level of confidence.

Compare the methods used in hypothesis tests and confidence intervals

b. The P-value method of hypothesis testing, the critical value method of hypothesis testing, along with confidence intervals all use the same distribution and standard error to derive results.

Thus, the results are expected to be equivalent in the sense that they result in the same conclusions.

Find the confidence level

c. It is desired to test the claim that the mean hemoglobin level in women is less than the mean hemoglobin level in men. The claim suggests a one-tailed hypothesis at a 0.01 level of significance.

Referring to 8-1, it can hence be concluded that the confidence level that is appropriate to test the claim is 98%.