Ankle Brachial Index. The ankle brachial index (ABI) compares the blood pressure of a patient's arm to the blood pressure of the patient's leg. The ABI can be an indicator of different diseases, including arterial diseases. A healthy (or normal) ABI is 0.9 or greater. In a study by M. McDermott et al. titled "Sex Differences in Peripheral Arterial Disease: Leg Symptoms and Physical Functioning" (Journal of the American Geriatrics Society, Vol. 51, No. 2, Pp. 222-228), the researchers obtained the ABI of 187 women with peripheral arterial disease. The results were a mean ABI of 0.64 with a standard deviation of 0.15 At the 1 % significance level, do the data provide sufficient evidence to conclude that, on average, women with peripheral arterial disease have an unhealthy ABI?

Check whether the data provide sufficient evidence to conclude that on average, women with peripheral arterial disease have an unhealthy ABI.

State the null and alternative hypothesis:

Null hypothesis:

$H_o:\mu =0.9$

That is, the data does not provide sufficient evidence to conclude that on average, women with peripheral arterial disease have an unhealthy ABI.

Alternative hypothesis:

$H_o:\mu <0.9$

That is, the data provide sufficient evidence to conclude that on average, women with peripheral arterial disease have an unhealthy ABI

Decide a significance level

Here, the significance level is,$\alpha =0.01$

Compute the value of the test statistic and P-value by using MINITAB.

MINITAB procedure:

Step 1: Choose Stat > Basic Statistics > 1-Sample t.

Step 2: In Summarized data, enter the sample size 187 and mean 0.64.

Step 3: In Standard deviation, enter a value 0.15.

Step 4: In Perform hypothesis test, enter the test mean as 0.9

Step 5: Check Options, enter Confidence level as99

Step 6: Choose less than in alternative.

Step 7: Click OK in all dialogue boxes.

MINITAB output:

One-Sample T

Test of mu$=0.9vs<0.9$

From the MINITAB output,

The value of test statistic is $-23.70$

The P-value is$0.000$

If $P\le \alpha$, then reject the null hypothesis.

Here, the P-value is 0.000 which is less than the level of significance. That is,

$P(=0.000)<\alpha (=0.01).$

Therefore, the null hypothesis is rejected at $1\%$level.

Thus, it can be conclude that the test results are statistically significant at $1\%$level of significance.

Interpretation:

Thus, the data provide sufficient evidence to conclude that on average, women with peripheral arterial disease have an unhealthy ABI