To determine the number of degrees of freedom for testing the difference between the mean earnings of men in California and New York, we follow these steps:
1. Identify the sample sizes from each group.
- The sample size for men in California is 123.
- The sample size for men in New York is 88.
2. Use the formula for calculating the degrees of freedom in a two-sample t-test which is given by:
[tex]\[
\text{Degrees of Freedom} = (n_1 + n_2 - 2)
\][/tex]
where [tex]\( n_1 \)[/tex] and [tex]\( n_2 \)[/tex] are the sample sizes of the two groups.
3. Plug in the sample sizes into the formula:
[tex]\[
\text{Degrees of Freedom} = 123 + 88 - 2
\][/tex]
4. Perform the calculation:
[tex]\[
\text{Degrees of Freedom} = 123 + 88 - 2 = 209
\][/tex]
Therefore, the number of degrees of freedom is 209.
