Question

In the paper "Depression and Bone Mineral Density: Is there a relationship in Elderly Asian Men?" S. Wong et al. published results of their study on bone mineral density (BMD) and depression for \(1999\) Hong Kong men aged \(65\) to \(92\) years. Here are the cross-classified data.

At the \(1%\) significance level, do the data provide sufficient evidence to conclude that BMD and depression are statistically dependent for elderly Asian men?

Short answer

The data provide is sufficient evidence to conclude that BMD and depression are statistically dependent for elderly Asian men.

Step-by-step solution

Step 1. Given information

The level of significance \(\alpha =0.01\)

Step 2. Calculation

Consider the below test hypothesis.

Null hypothesis:

\(H_{0}\): There is no association between BMD and depression.

Alternative hypothesis:

\(H_{a}\):There is association between BMD and depression.

By using any software perform the chi-square homogeneity test to find the test statistic.

Enter the given data,

Then we get, the chi-square static as \(10.095, p-value=0.006\)

Then, we have the

the rejection rule:

\(p-value \leq \alpha\), then null hypothesis rejected.

The level of significance \(\alpha =0.01\)

Here , clearly \(p-\)value is less than the level of significance.

\(p-value (0.006)<\alpha (0.01)\)

So, the null hypothesis is rejected at \(1%\) significant level.

Thus the results are statistically significant at \(1%\) significant level.

Hence,

The data provide is sufficient evidence to conclude that BMD and depression are statistically dependent for elderly Asian men.