Chapter 8.1, Problem 28E

Testing a Difference Other Than Zero Sometimes a researcher is interested in testing a difference in means other than zero. In Exercises 27 and 28, you will test the difference between two means using a null hypothesis of H₀: μ₁ − μ₂ = k, H₀: μ₁ − μ₂ ≥ k, or H₀: μ₁ − μ₂ ≤ k. The standardized test statistic is still

$\text{z}\text{=}\frac{({\bar{x}}_1-{\bar{x}}_2)-({\mu }_1-{\mu }_2)}{{\sigma }_{{\bar{x}}_1-{\bar{x}}_2}}where{\sigma }_{{\bar{x}}_1-{\bar{x}}_2}=\sqrt{\frac{{\sigma }_1^2}{n_1}+\frac{{\sigma }_2^2}{n_2}.}$

28. Architect Salaries Is the difference between the mean annual salaries of entry level architects in Denver, Colorado, and Los Angeles, California, equal to $10,000? To decide, you select a random sample of entry level architects from each city. The results of each survey are shown in the figure. Assume the population standard deviations are σ₁ = $6520 and σ₂ = $7130. At α = 0.01, what should you conclude? (Adapted from Salary.com)