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. In a​ study, researchers obtained the ABI of 187 women with arterial disease. The results were a mean ABI of 0.89 with a standard deviation of 0.13 . At the 10 ​% significance​ level, do the data provide sufficient evidence to conclude​ that, on​ average, women with arterial disease have an unhealthy​ ABI?

Answer 1

A healthy ( or normal) ABI is 0.9 or greater

No.of women (n) = 187

mean ABI of women = 0.89

standard deviation = 0.13

Null hypothesis H0 : the mean healthy of ABI is 0.9

Alternative hypothesis H1 : the mean ABI < 0.9

test statistic (z) =

                  = 0.89 ; = 0.9

                  σ= 0.13      ;

plug the values and simplify

the z value = -1.0519

P(z < -1.0519) = 0.1464

We fail to Reject the NULL hypothesis at 10% levl of significance

so data provide insufficient evidence to conclude that women with peripheral arterial disease have an unhealthy ABI

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