\"Testing the Difference Between Two Means.\" ( Note : Please respond to one [1]

Question

"Testing the Difference Between Two Means." (Note: Please respond to one [1] of the following two [2] bulleted items)

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 1 and 2?

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.

Explanation / Answer

Solution:

The assumptions required to use the z test to test differences between two means are as follows:

The samples are independent; that is, observations in population 1 are not affected by observations in population 2, and vice versa.

The set of differences between sample means is normally distributed. This assumption will automatically hold if the sample sizes are large.

The size of each population is large relative to the sample drawn from the population. That is, N1is large relative to n1, and N2 is large relative to n2.

If the population standard deviations are unknown, we can use the sample standard deviation. But in this case, we will lose one degree of freedom.

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