Suppose Connie owns a pet store in a large community that has over 50,000 pet owners. She believes that the proportion of men who own cats is different from the proportion of women who own cats. Connie decides to test this claim by performing a two-sample ?-test for two proportions. Her hypotheses are given by ?0:??=???1:??≠?? where ?0 is the null hypothesis, and ?1 is the alternative hypothesis. The variables ?? and ?? represents the population proportion of men and women cat owners, respectively. She randomly samples 420 men and 493 women who are pet owners in the community and finds that 234 men own cats and 256 women own cats. Determine the pooled sample proportion, ?̂. Provide your answer precise to three decimal places. Compute the standard error of the difference of the sample proportions (SE). Provide your answer precise to three decimal places. SE =     ?̂=

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