A researcher would like to determine if the proportion of households without health Heath Insurance insurance coverage differs with household income. Suppose the following data were Household Income Yes No collected from 700 randomly selected households. Complete parts a through c. Less than $25,000 53 24 $25,000 to $49,999 145 40 $50,000 to $74,999 200 40 $75,000 or more 172 26 a. Using a = 0.01, perform a chi-square test to determine if the proportion of households without health insurance differs by income bracket. Choose the correct null and alternative hypotheses below. O A. Ho: Not all p's are equal O B. Ho: P1 = P2 = P3 = P4 H1: P1 = P2 = P3 = P4 H1 : P1 # P2 # P3 * P4 O C. Ho: P1 # P2 # P3 # P4 &D. Ho: P1 = P2 = P3 = P4 H1: P1 = P2 = P3 = P4 H1: Not all p's are equal at is the test stati x2 = 13.67 (Round to two decimal places as needed.) What is the critical value? (6.01 = 11.34 (Round to two decimal places as needed.) State the conclusion. Reject Ho. There is sufficient evidence that the proportion of households without health insurance differs by income bracket. b. Interpret the meaning of the p-value. What is the p-value? p-value = 0.003 (Round to three decimal places as needed.) What does the p-value mean? Select the correct choice and fill in the answer box to complete your choice. (Round to one decimal place as needed.) A. Given a very large number of samples, there is a % chance of observing a sample with the given data. O B. There is a % chance of observing a test statistic value greater than the actual test statistic value if there is no difference in the proportion of households without health insurance O C. There is a % chance of rejecting the null hypothesis when it should not be rejected