Question

The ankle brachial index (ABI) compares the blood pressure of a patient’s arm to the blood pressure of the patient’s leg. A healthy ABI is 0.9 or greater. A study obtained the ABI of 51 women. The results were a mean ABI of 0.64 with a sample standard deviation of 0.15. Does the data provide sufficient evidence to conclude that, on average, women with peripheral arterial disease have an unhealthy ABI? , identify the null hypothesis, alternative hypothesis, test statistic, critical value, P-value, and conclusion about the null hypothesis. Sketch a normal distribution to show your results. Use a significance level of  = 0.05.

Answer 1

As we are testing here whether the data provide sufficient evidence to conclude that, on average, women with peripheral arterial disease have an unhealthy ABI, therefore the null and the alternative hypothesis here are given as:

The test statistic here is computed as:

As the test statistic value here is very very low, therefore the p-value would be approximately 0. Therefore the test is significant here and we can reject the null hypothesis here. Therefore we have sufficient evidence here that on average, women with peripheral arterial disease have an unhealthy ABI

The shaded region is to the left, but it is so small that it is not visible on the graph above.