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What two assumptions must be met when you are using the z test to test differences between two means? Can the sample standard deviations s1 and s2 be used in place of the population standard deviations σ1 and σ2?

Retired workers and disabled workers both receive Social Security benefits. What information would we need to test the claim that the difference in monthly benefits between the two groups is greater than $30 at the 0.05 level of significance? Write out the hypotheses and explain the testing procedure.

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