A vaccine is available to prevent the contraction of human...

A vaccine is available to prevent the contraction of human papillomavirus (HPV). The Centers for Disease Control and Prevention recommends this vaccination for all young girls in two doses. In a 2015 study reported in the Journal of American College Health, Lee et al. studied vaccination rates among Asian American and Pacific Islander (AAPI) women and non-Latina white women. Data are shown in the table. Test the hypothesis that vaccination rates and race are associated. Use a $0.05$ significance level. $$\begin{array}{|lcc|}\hline \text { Completed HPV vaccinations } & \text { AAPI } & \text { White } \\\hline \text { Yes } & 136 & 1170 \\ \hline \text { No } & 216 & 759 \\\hline\end{array}$$

A vaccine is available to prevent the contraction of human papillomavirus (HPV). The Centers for Disease Control and Prevention recommends this vaccination for all young girls in two doses. In a 2015 study reported in the Journal of American College Health, Lee et al. studied vaccination rates among Asian American and Pacific Islander (AAPI) women and non-Latina white women. Data are shown in the table. Test the hypothesis that vaccination rates and race are associated. Use a $0.05$ significance level.
$$\begin{array}{|lcc|}\hline \text { Completed HPV vaccinations } & \text { AAPI } & \text { White } \\\hline \text { Yes } & 136 & 1170 \\
\hline \text { No } & 216 & 759 \\\hline\end{array}$$

Key Concepts

Significance Level and p-Value

The significance level, often denoted by alpha (?), is a threshold set by the researcher (commonly 0.05) for determining when to reject the null hypothesis. The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. If the p-value is less than the chosen significance level, the null hypothesis is rejected, indicating an association between the variables.

Degrees of Freedom

Degrees of freedom refer to the number of values in the final calculation of a statistic that are free to vary. In the context of a chi-squared test applied to a contingency table, the degrees of freedom are calculated as the product of one less than the number of rows and one less than the number of columns, influencing the shape of the chi-squared distribution used for determining significance.

Contingency Table Analysis

Contingency table analysis involves organizing categorical data into a table format where the frequency of different combinations of categories is displayed. This approach is commonly used to assess the relationship between two categorical variables by comparing observed frequencies to what would be expected if the variables were independent.

Hypothesis Testing

Hypothesis testing is a statistical method used to determine whether there is enough evidence in a sample of data to infer that a certain condition holds for the entire population. It typically involves formulating a null hypothesis that represents no effect or no association and an alternative hypothesis that represents the effect or association being tested.

Chi-Squared Test of Independence

The chi-squared test of independence is a statistical test that evaluates whether there is a significant association between two categorical variables in a contingency table. It compares the observed counts in each cell of the table to the expected counts calculated under the assumption that the row and column variables are independent.

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