Question

4. Based on the following information describing the distribution of fear of crime among a group of students, determine if fear of crime varies by gender… [chi-sq. = 20.03]

	Male	Female
Safe	100	81
Unsafe	33	82

1. Formulate the null and research/alternative hypotheses.
2. Calculate the chi-square
3. Report the critical chi-square at the corresponding probability level [.05]and degrees of freedom
4. Test the null hypothesis and reach a statistical conclusion;
5. Interpret your results

Answer 1

Solution:-

4)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: p_Male = P_Female (For safe)

Alternative hypothesis: p_MaleP_Female

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for homogeneity.

Analyze sample data. Applying the chi-square test for homogeneity to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = (r - 1) * (c - 1) = (2 - 1) * (2 - 1)
D.F = 1
E_r,c = (n_r * n_c) / n

Χ² = 20.04

Χ²_Critical = 3.838

where DF is the degrees of freedom, r is the number of populations, c is the number of levels of the categorical variable, n_r is the number of observations from population r, n_c is the number of observations from level c of the categorical variable, n is the number of observations in the sample, E_r,c is the expected frequency count in population r for level c, and O_r,c is the observed frequency count in population r for level c.

Interpret results. Since the Χ²-value (20.04) lies in rejection region, hence have to we reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that fear of crime varies by gender.