Question

Fear of Gangs. In the article "Growing Pains and Fear of Gangs" (Applied Psychology in Criminal Justice, Vol. 5, No. 2, pp. 139-164), 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.

Short answer

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 at the 1% significance level.

Step-by-step solution

Step 1. Given information

Step 2. 

Check whether or not 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.

Step 1:

The test hypotheses are given below:

Null hypothesis:

H0 : There is no association exists between worry about a gang attack and actually being a victim of a gang attack.

Alternative hypothesis:

H1 : There is an association exists between worry about a gang attack and actually being a victim of a gang attack.

Step 2: Decide the level of significance.

Here, the level of significance is, 1%

Step 3:

Find the expected frequency and test statistic.

MINITAB procedure:

Step 1: Choose Stat > Tables > Chi-Square test for association.

Step 2: In Columns containing the table, enter the column of Yes and No.

Step 3: In Rows, select Victim.

Step 4: Under Statistics, select Chi-square test, Display counts in each cell, Display marginal counts and expected cell counts.

Step 5: Click OK.

Now,

Minitab output

Pearson Chi-Square $=23.455,\mathrm{DF}=1,\mathrm{p}-\mathrm{Value}=0.000$

Likelihood Ratio Chi-Square=19.841, DF=1, p-Value =0.000

From the MINITAB output, the value of the chi-square statistic is 23.455.

Step 4:

Find the p-value.

From the MINITAB output, the p-value is 0.000

Step 5:

Rejection rule:

If , then reject the null hypothesis.

Here, the P-value is lesser than the level of significance.

That is, P-value (=0.000)<alpha(=0.01).

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

Thus, the results are statistically significant at 1% level of significance.

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 at the 1% significance level.