A researcher compares the typical family size in 10 cultures, 5 from Language Group A and 5 from Language Group B. The figures for the Group A cultures are 1.2, 2.5, 4.3, 3.8, and 7.2. The figures for the Group B cultures are 2.1, 9.2, 5.7, 6.7, and 4.8. Based on these 10 cultures, does typical family size differ in cultures with different language groups? Use the .05 level.
(a) Carry out a t test for independent means using the actual scores.
(b) Carry out a square-root transformation (to keep things simple, round off the transformed scores to one decimal place).
(c) Carry out a t test for independent means using the transformed scores.
(d) Explain what you have done and why to someone who is familiar with the t test for independent means but not with data transformation.