A researcher wants to determine if the average performance on a standardized business management test is significantly less for students with undergraduate degrees in engineering as compared with the students with undergraduate degrees in liberal arts. The data on the sample sizes, the means of independent samples from the two populations, and the standard deviations are summarized below:
Engineering Liberal Arts
1 = 21.45 2 = 24.6
σ1 = 3.46 σ2 = 2.99
n1 = 50 n2 = 50
If the level of significance is 0.05, what is critical value to set up the decision rule to test the claim that the liberal arts students perform better than engineering students on average?
2.33
2.57
1.28
1.96
1.65