Random Timing

     1. At a Midwestern   hospital there were a total of 932 births in 20 consecutive weeks. Of these   births, 216 occurred on weekends. Do these data reveal more than chance   deviation from random timing of the births (weekday and weekend)? Use = 0.05.    

     2. Exercise 14.36   (p. 620-621) Physical Fitness in the U.S. A survey was conducted to   investigate the interest of middle-aged adults in physical fitness programs   in Rhode Island, Colorado, California, and Florida. The objective of the   investigation was to determine whether adult participation in physical   fitness programs varies from one region of the United States to another. A   random sample of people were interviewed in each state and these data were   recorded:      Rhode Island Colorado California Florida   Participate 46 63 108 121   Do not participate 149 178 192 179      Do the data indicate a difference in   adult participation in physical fitness programs from one state to another?   If so, describe the nature of the differences.    

     3. Exercise 14.40   (p.621) 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. 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<0.0001).      Prone Supine or side   Number of Infants 121 199   Number who roll over 93 119    

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

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

c.) Compare the results of part 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.