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.

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.

You need the standard deviation. However, I'll leave the rest to you.

We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.

To test the claim that the difference in monthly benefits between retired workers and disabled workers is greater than $30 at the 0.05 level of significance, we need the following information:

1. Sample data: We would need a random sample of monthly benefit amounts for both retired and disabled workers. The sample should be representative of the target population.

2. Sample sizes: We need to know the number of retired workers and disabled workers in the sample.

3. Significance level: The claim states a significance level of 0.05, which means we want the likelihood of observing a difference greater than $30 by chance to be less than 5%.

Now let's set up the hypothesis and explain the testing procedure:

Hypotheses:
- Null Hypothesis (H0): The difference in monthly benefits between retired workers and disabled workers is not greater than $30.
- Alternative Hypothesis (Ha): The difference in monthly benefits between retired workers and disabled workers is greater than $30.

Testing Procedure:
1. Calculate the difference in monthly benefit amounts between retired workers and disabled workers for each observation in your sample.
2. Find the mean and standard deviation of the differences.
3. Use the obtained mean and standard deviation to calculate the test statistic, which is the difference in means divided by the standard deviation.
4. Determine the critical value associated with a significance level of 0.05. This critical value represents the cutoff point beyond which we would reject the null hypothesis.
5. Compare the test statistic to the critical value. If the test statistic is greater than the critical value, we reject the null hypothesis in favor of the alternative hypothesis. If not, we fail to reject the null hypothesis.
6. Finally, calculate the p-value associated with the test statistic. If the p-value is less than 0.05, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

Remember, to perform this test, you would need access to the necessary data and statistical tools such as a statistical software program or mathematical calculations.