Chapter 8.1, Problem 27E

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

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

27. Software Engineer Salaries Is the difference between the mean annual salaries of entry level software engineers in Raleigh, North Carolina, and Wichita, Kansas, more than $2000? To decide, you select a random sample of entry level software engineers from each city. The results of each survey are shown in the figure at the left. Assume the population standard deviations are σ₁ = $10,850 and (σ₂ = $10,970. At α = 0.05, what should you conclude? (Adapted from Salary.com)