Question

In the article "Growing Pains and Fear of Gangs", B. Brown and W. Benedict examined the relationship between worry about a gang attack and actually being a victim of a gang attack. Interviews of a sample of high school students yielded the following contingency table.

At the \(1%\) significance level, do the data provide sufficient evidence to conclude that an association exists between worry about a gang attack and actually being a victim of a gang attack?

Short answer

The data provide is sufficient evidence to conclude that worry about gang attack and actually being a victim of a gang attack.

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 worry about gang attack and actually being a victim of a gang attack

Alternative hypothesis:

\(H_{a}\): There is association between worry about gang attack and actually being a victim of a gang attack.

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 \(=23.455, p-value=0.00\)

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.

\(p-value (0.00)<\alpha (0.01)\)

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 worry about gang attack and actually being a victim of a gang attack.