Question

what is the chi square value and p value for this data

Non-Hispanic, White Non-White Race Barrier status Barrier present 29 No barrier Total 162 81.00% 19.00% 100% 90.63% 9.37 100% 38 200 32

Answer 1

Solution:-

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

H₀: Race and barrier status are independent.
H_a: Race and barrier status are not independent.

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

Analyze sample data. Applying the chi-square test for independence 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

$\chi ^{2}=\sum \left [\frac{(O_{r,c}-E_{r,c})^{2}}{E_{r,c}} \right ]$

Χ² = 1.76

where DF is the degrees of freedom.

The P-value is the probability that a chi-square statistic having 1 degrees of freedom is more extreme than 1.76.

We use the Chi-Square Distribution Calculator to find P(Χ² > 1.76) = 0.185

Interpret results. Since the P-value (0.185) is greater than the significance level (0.05), we failed to reject the null hypothesis.

Thus, we conclude that there is a relationship between race and barrier status.