91Ó°ÊÓ

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:

$H_o:\mathrm{μ}=0.9$

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:

$H_o:\mathrm{μ}<0.9$

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,$\mathrm{Î\pm }=0.01$

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 $P≤\mathrm{Î\pm }$, then reject the null hypothesis.

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

$P(=0.000)<\mathrm{Î\pm }(=0.01).$

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