4. Baby’s Sleeping Position 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.15 The baby’s predominant sleep position—

either on the stomach or 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 back position were less likely to roll over at the 4-month checkup than infants who slept primarily in the stomach position (P

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

b. Rewrite the sample data as a 232 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 5X2 and that the critical values for rejecting 0 H have the same relationship.

d. Find the p-value for the large-sample z-test in part a.
Compare this p-value with the p-value for the chisquare test, shown on the TI-84 Plus screen.

Stomach Side or Back Number of Infants 121 199 Number Who Roll Over 93 119