Does a baby's sleeping position affect the development of motor skills? In one study, 343 full-term infants were examined at their 4-month checkup for various developmental milestones, such as rolling over, grasping a rattle, and reaching for an object. 14 The baby's predominant sleep position-either prone (on the stomach) or supine (on the back) or side-was determined by a telephone interview with the parent. The sample results for 320 of the 343 infants for whom information was received are shown in the table. The researcher reported that infants who slept in the side or supine position were less likely to roll over at the 4-month checkup than infants who slept primarily in the prone position (P< .001).

a. Use a large-sample z-test to confirm or refute the researcher's conclusion.

b. Rewrite the sample data as a 2x2 contingency table. Use the chi-square test for homogeneity to confirm or refute the researcher's conclusion.

c. Compare the results of parts a and b. Confirm that the two test statistics are related as z2 = x2 and that the critical values for rejecting H0 have the same relationship.