The average monthly Social Security benefit in 2004 for retired workers was $954.90 and for disabled workers was $894.10. Researchers used data from the Social Security records to test the claim that the difference in monthly benefits between the two groups was greater than $30. Based on the following information, can the researchers€™ claim be supported at the 0.05 level of significance?

a. State the hypotheses and identify the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
e. Summarize the results.

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Sample size Mean benefit Population standard deviation Retired Disabled 60 $960.50 $902.89 S98 60 $101